C₂×#22552 #6379639

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

4154 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 5 generators on 22 points:

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

maximal subgroup of	C₂×#6577292, C₂×#6668300, C₂×#6388812, …
maximal normal subgroup of	C₂×#6577292, C₂×#6668300, C₂×#6388812, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6286835);