C₅×C₂₃×D₁₁₇ #41002085

order	26910
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₃×D₁₁₇
unambiguous semidirect product	C₉⋊(C₅×C₂₃×D₁₃)
unambiguous semidirect product	C₁₃⋊(C₅×D₉×C₂₃)

	subgroup	G/H
center, hypercenter	C₅×C₂₃	D₁₁₇
commutator, cosocle, hypocenter	C₉×C₁₃	C₂×C₅×C₂₃
Frattini	C₃	C₅×C₂₃×D₃₉
Fitting	C₅×C₉×C₁₃×C₂₃	C₂
socle	C₃×C₅×C₁₃×C₂₃	D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₅×C₂₃

48 conjugacy classes of subgroups.

μ_t(G) = 13455

6900 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 12);