C₅×C₂₉×C₇₉⋊C₃ #46805386

order	34365
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₉×C₇₉⋊C₃
unambiguous semidirect product	C₇₉⋊(C₃×C₅×C₂₉)
unambiguous semidirect product	(C₅×C₇₉)⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂₉×C₇₉)⋊(C₃×C₅)
unambiguous semidirect product	(C₅×C₂₉×C₇₉)⋊C₃

	subgroup	G/H
center, hypercenter	C₅×C₂₉	C₇₉⋊C₃
commutator, cosocle, hypocenter	C₇₉	C₃×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₂₉×C₇₉	C₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₅×C₂₉

16 conjugacy classes of subgroups.

μ_t(G) = 11455

4205 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34365, 2);