C₂²⋊Q₈×C₄₈₇ #29510098

order	15584
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₈₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊Q₈×C₄₈₇
unambiguous semidirect product	C₂²⋊(Q₈×C₄₈₇)

	subgroup	G/H
center, socle	C₂²×C₄₈₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₄₈₇
prime radical	C₂³×C₄₈₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₈₇ ◁ G

74 conjugacy classes of subgroups.

μ_t(G) = 7792

6818 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15584, 29);