C₅×C₇×C₁₃×D₃₇ #46797598

order	33670
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₇×C₁₃×D₃₇
unambiguous semidirect product	C₃₇⋊(C₂×C₅×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₇×C₁₃	D₃₇
commutator, cosocle, hypocenter	C₃₇	C₂×C₅×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₃₇	C₂
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₅×C₇×C₁₃

32 conjugacy classes of subgroups.

μ_t(G) = 16835

9100 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33670, 2);