C₅⋊(C₂₉⋊(D₁₃⋊C₉)) #46800238

order	33930
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₅⋊(C₂₉⋊(D₁₃⋊C₉))
unambiguous semidirect product	C₂₉⋊(C₅⋊(D₁₃⋊C₉))
unambiguous semidirect product	(C₁₃⋊C₉)⋊D₁₄₅
unambiguous semidirect product	D₁₈₈₅⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅⋊(C₂₉⋊(D₁₃⋊C₃))
commutator, hypocenter	C₅×C₁₃×C₂₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₃×C₂₉	C₂×C₃
prime radical	C₃×D₁₈₈₅	C₃
LCS	G ▷ C₅×C₁₃×C₂₉
UCS	C₁ ◁ C₃

48 conjugacy classes of subgroups.

μ_t(G) = 16965

Polycyclic presentation:

2,3,5,13,29,3|b^3=f,c^a=c^4,d^a=d^12,e^a=e^28,d^b=d^3

1536 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33930, 24);