C₅×D₇×D₇₉⋊C₃ #45684422

order	33180
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₅×D₇×D₇₉⋊C₃
unambiguous semidirect product	D₇₉⋊(C₃×C₅×D₇)
unambiguous semidirect product	(C₇×D₇₉⋊C₃)⋊(C₂×C₅)
unambiguous semidirect product	(D₇×C₇₉⋊C₃)⋊(C₂×C₅)
unambiguous semidirect product	((C₇₉⋊C₃)⋊D₇)⋊(C₂×C₅)

	subgroup	G/H
center, hypercenter	C₅	D₇×D₇₉⋊C₃
commutator, cosocle, hypocenter	C₇×C₇₉	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₇₉	C₂²×C₃
LCS	G ▷ C₇×C₇₉
UCS	C₁ ◁ C₅

80 conjugacy classes of subgroups.

μ_t(G) = 2765

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 53);