C₂×C₇⋊D₇×C₁₆₇ #45658619

order	32732
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆₇ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₇⋊D₇×C₁₆₇
unambiguous semidirect product	(C₂×C₇)⋊(D₇×C₁₆₇)

	subgroup	G/H
center, hypercenter	C₂×C₁₆₇	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂²×C₁₆₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₆₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₁₆₇

100 conjugacy classes of subgroups.

μ_t(G) = 16366

8684 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32732, 27);