C₂²×#7554 #72321908

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄³ · Schur multiplier (H₂) = C₂¹⁴×C₄

Aliases

123269 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 24 points:

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

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

maximal subgroup of	C₂²×#153827, C₂²×#153831, C₂²×C₂²⋊C₄×#95, …
maximal normal subgroup of	C₂²×#153827, C₂²×#153831, C₂²×C₂²⋊C₄×#95, …

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

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