C₂×C₇×C₁₃×C₆₇⋊C₃ #49143333

order	36582
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇×C₁₃×C₆₇⋊C₃
unambiguous semidirect product	(C₂×C₆₇)⋊(C₃×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₃	C₆₇⋊C₃
commutator, cosocle, hypocenter	C₆₇	C₂×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₃×C₆₇	C₃
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₇×C₁₃

32 conjugacy classes of subgroups.

μ_t(G) = 12194

4550 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36582, 2);