C₂×C₇×D₉×C₁₂₇ #44544694

order	32004
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₂₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×D₉×C₁₂₇
unambiguous semidirect product	C₉⋊(C₂²×C₇×C₁₂₇)
unambiguous semidirect product	(C₂×C₉)⋊(C₂×C₇×C₁₂₇)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₂₇	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₇×C₁₂₇
Frattini	C₃	C₂×D₃×C₇×C₁₂₇
Fitting	C₂×C₇×C₉×C₁₂₇	C₂
socle	C₂×C₃×C₇×C₁₂₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₇×C₁₂₇

60 conjugacy classes of subgroups.

μ_t(G) = 16002

10668 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 76);