It´s always hard to write sth. about ones own favourite anime;
Probably the last humans fight some alien race/monsters; permanently on the edge of extinction on a gigantic space ship; Planet earth seems to be gone!
Amazing space action? Got it!
Friendship till death tears it apart? Got it!
Group dynamics? Got it!
Slice of life? Got it!
Social problems/questions? Got it!
Comedy? Yes even that!
What else: Some romance (not finished), some conspiracy, politics etc.
All on a level where you never think it´s stupid; The MC is a little bit dense (girls) but a "battle ace". Did not find an anime yet, that was soo catchy from the beginning to the end. If at first you think the MC is an idiot, give him 2-3 episodes; he`ll get cool!
PS: Never listen to the intro song when driving on the highway; You`ll speed up automatically!