C₅×C₇×C₃⋊D₃×C₃₇ #37552142

order	23310
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇×C₃₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₇×C₃⋊D₃×C₃₇
unambiguous semidirect product	C₃⋊(C₅×D₃×C₇×C₃₇)

	subgroup	G/H
center, hypercenter	C₅×C₇×C₃₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₇×C₃₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₇×C₃₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₇×C₃₇

96 conjugacy classes of subgroups.

μ_t(G) = 11655

7770 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23310, 161);