C₂×C₅×D₃×C₁₃×C₂₉ #36383239

order	22620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₁₃×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₃×C₁₃×C₂₉
unambiguous semidirect product	C₃⋊(C₂²×C₅×C₁₃×C₂₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₅×C₁₃×C₂₉)

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₃×C₂₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₅×C₁₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₁₃×C₂₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₅×C₁₃×C₂₉

80 conjugacy classes of subgroups.

μ_t(G) = 11310

11310 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 169);