C₄×#1375 #146297

order	512
nilpotency class	2
isoclinism	isoclinic class of H(3,ℤ/4)
automorphism	?
homology	Abelianization (H₁) = C₄²×C₈ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

802 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 3 generators on 24 points:

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

maximal subgroup of	#72309582, C₄×#13037, D₄×#1375, …
maximal normal subgroup of	#72309582, C₄×#13037, D₄×#1375, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 53493);