C₂×C₃²×D₇×C₁₂₇ #44544919

order	32004
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₁₂₇ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₂×C₃²×D₇×C₁₂₇

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₂₇	D₇
commutator, cosocle, hypocenter	C₇	C₂²×C₃²×C₁₂₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₂₇	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃²×C₁₂₇

120 conjugacy classes of subgroups.

μ_t(G) = 16002

11430 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 301);