C₅×D₇×D₇₃⋊C₃ #44501298

order	30660
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₇×D₇₃⋊C₃
unambiguous semidirect product	D₇₃⋊(C₃×C₅×D₇)
unambiguous semidirect product	(C₇×D₇₃⋊C₃)⋊(C₂×C₅)
unambiguous semidirect product	(D₇×C₇₃⋊C₃)⋊(C₂×C₅)
unambiguous semidirect product	((C₇₃⋊C₃)⋊D₇)⋊(C₂×C₅)

	subgroup	G/H
center, hypercenter	C₅	D₇×D₇₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₇₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₇₃	C₂²×C₃
LCS	G ▷ C₇×C₇₃
UCS	C₁ ◁ C₅

80 conjugacy classes of subgroups.

μ_t(G) = 2555

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 61);