C₄×#2850 #607626

order	512
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

4750 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 20 points:

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

maximal subgroup of	#72306074, #72306076, C₄×#36096, …
maximal normal subgroup of	#72306074, #72306076, C₄×#36096, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 514822);