C₂²×C₄×#347 #72313340

order	1024
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄³ · Schur multiplier (H₂) = C₂⁷×C₄²

Aliases

C₂²×C₄×#347

6637 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 256

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

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

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

maximal subgroup of	C₂²×C₄×AGL(1,ℤ/16), C₂²×#496124, C₂²×D₄×#347
maximal normal subgroup of	C₂²×C₄×AGL(1,ℤ/16), C₂²×#496124, C₂²×D₄×#347

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

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