C₂×C₃×D₅×C₁₃×C₄₁ #44544489

order	31980
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₃×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃×D₅×C₁₃×C₄₁
unambiguous semidirect product	C₅⋊(C₂²×C₃×C₁₃×C₄₁)
unambiguous semidirect product	(C₂×C₅)⋊(C₂×C₃×C₁₃×C₄₁)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃×C₄₁	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃×C₁₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃×C₄₁	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₁₃×C₄₁

80 conjugacy classes of subgroups.

μ_t(G) = 15990

12792 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 217);