C₅⋊(C₂₃⋊(D₁₃⋊C₉)) #41002097

order	26910
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₅⋊(C₂₃⋊(D₁₃⋊C₉))
unambiguous semidirect product	C₂₃⋊(C₅⋊(D₁₃⋊C₉))
unambiguous semidirect product	(C₁₃⋊C₉)⋊D₁₁₅
unambiguous semidirect product	D₁₄₉₅⋊C₉

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₅⋊(C₂₃⋊(D₁₃⋊C₃))
commutator, hypocenter	C₅×C₁₃×C₂₃	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₃×C₂₃	C₂×C₃
prime radical	C₃×D₁₄₉₅	C₃
LCS	G ▷ C₅×C₁₃×C₂₃
UCS	C₁ ◁ C₃

48 conjugacy classes of subgroups.

μ_t(G) = 13455

Polycyclic presentation:

2,3,5,13,23,3|b^3=f,c^a=c^4,d^a=d^12,e^a=e^22,d^b=d^3

1221 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 24);