C₂²⋊Q₈×C₄₆₇ #28417836

order	14944
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₆₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊Q₈×C₄₆₇
unambiguous semidirect product	C₂²⋊(Q₈×C₄₆₇)

	subgroup	G/H
center, socle	C₂²×C₄₆₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₄₆₇
prime radical	C₂³×C₄₆₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₆₇ ◁ G

74 conjugacy classes of subgroups.

μ_t(G) = 7472

6538 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14944, 29);