C₅×C₇×D₁₃×C₃₇ #46797599

order	33670
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₇×D₁₃×C₃₇
unambiguous semidirect product	C₁₃⋊(C₂×C₅×C₇×C₃₇)

	subgroup	G/H
center, hypercenter	C₅×C₇×C₃₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₅×C₇×C₃₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃×C₃₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₇×C₃₇

32 conjugacy classes of subgroups.

μ_t(G) = 16835

10360 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33670, 3);