C₂×C₅×D₃×C₁₃×C₃₁ #37564006

order	24180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₃×C₃₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₃×C₁₃×C₃₁
unambiguous semidirect product	C₃⋊(C₂²×C₅×C₁₃×C₃₁)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₅×C₁₃×C₃₁)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃×C₃₁	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₁₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃×C₃₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₃×C₃₁

80 conjugacy classes of subgroups.

μ_t(G) = 12090

12090 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 305);