C₂⁶×D₄ #10587006

order	512
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁸ · Schur multiplier (H₂) = C₂²⁸

Aliases

direct product	C₂⁶×D₄
unambiguous semidirect product	C₄⋊C₂⁷
unambiguous semidirect product	C₂²⋊C₂⁷

	subgroup	G/H
center, socle	C₂⁷	C₂²
commutator, Frattini, cosocle	C₂	C₂⁸
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂ ▷ C₁

805186 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 8 generators on 16 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10494202);