C₃×D₇×D₁₂₇⋊C₃ #44544813

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

Aliases

direct product	C₃×D₇×D₁₂₇⋊C₃
unambiguous semidirect product	D₁₂₇⋊(C₃²×D₇)

	subgroup	G/H
center, hypercenter	C₃	D₇×D₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₂₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₂₇	C₂²×C₃
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₃

120 conjugacy classes of subgroups.

μ_t(G) = 2667

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 195);