C₂×C₄×#548 #7625389

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₄ · Schur multiplier (H₂) = C₂¹⁴

Aliases

12242 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 6 generators on 18 points:

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

maximal subgroup of	C₂×C₄×D₄×#41, C₂×#7666944, C₂×C₄×#3488, …
maximal normal subgroup of	C₂×C₄×D₄×#41, C₂×#7666944, C₂×C₄×#3488, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532585);