C₂×C₄×#520 #7625213

order	512
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄² · Schur multiplier (H₂) = C₂¹³×C₄

Aliases

14234 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);(7,8,9,10)(11,12)(13,17)(14,15)(16,18);(12,15)(16,17);(11,12)(13,16)(14,15)(17,18);(11,13,14,18)(12,16,15,17)

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

maximal subgroup of	C₂×#7625633, C₂×C₄×#3488, C₂×#7629439, …
maximal normal subgroup of	C₂×#7625633, C₂×C₄×#3488, C₂×#7629439, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532409);