C₄⋊Q₈×C₄₅₇ #28410441

order	14624
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₅₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₄⋊Q₈×C₄₅₇
unambiguous semidirect product	C₄⋊(Q₈×C₄₅₇)

	subgroup	G/H
center, socle, prime radical	C₂²×C₄₅₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₄₅₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₅₇ ◁ G

68 conjugacy classes of subgroups.

μ_t(G) = 14624

6398 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14624, 35);