C₅⋊(C₄₇⋊(D₇⋊C₉)) #44444087

order	29610
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₅⋊(C₄₇⋊(D₇⋊C₉))
unambiguous semidirect product	C₄₇⋊(C₅⋊(D₇⋊C₉))
unambiguous semidirect product	(C₇⋊C₉)⋊D₂₃₅
unambiguous semidirect product	D₁₆₄₅⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅⋊(ΓL(1,𝔽₈)⋊D₄₇)
commutator, hypocenter	C₅×C₇×C₄₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₇×C₄₇	C₂×C₃
prime radical	C₃×D₁₆₄₅	C₃
LCS	G ▷ C₅×C₇×C₄₇
UCS	C₁ ◁ C₃

48 conjugacy classes of subgroups.

μ_t(G) = 14805

Polycyclic presentation:

2,3,5,7,47,3|b^3=f,c^a=c^4,d^a=d^6,e^a=e^46,d^b=d^2

1776 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29610, 24);