C₂⁴×#334 #72286586

order	1024
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₈ · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂⁴×#334

23349 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1024

A minimal faithful permutation representation — 6 generators on 24 points:

(1,2);(3,4);(10,13)(11,15)(14,16)(17,18,19,21,20,22,23,24);(5,6);(9,10,11,13,12,14,15,16);(7,8)

448 conjugacy classes. The character table is too large to display.

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((1,2), (3,4), (10,13)(11,15)(14,16)(17,18,19,21,20,22,23,24), (5,6), (9,10,11,13,12,14,15,16), (7,8));