C₅×C₇×D₉×C₄₇ #44444073

order	29610
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₇×D₉×C₄₇
unambiguous semidirect product	C₉⋊(C₂×C₅×C₇×C₄₇)

	subgroup	G/H
center, hypercenter	C₅×C₇×C₄₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₅×C₇×C₄₇
Frattini	C₃	C₅×D₃×C₇×C₄₇
Fitting	C₅×C₇×C₉×C₄₇	C₂
socle	C₃×C₅×C₇×C₄₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₅×C₇×C₄₇

48 conjugacy classes of subgroups.

μ_t(G) = 14805

9870 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 10);