C₂₃×D₉₉ #17986909

order	4554
isoclinism	isoclinic class of D₉₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×D₉₉
unambiguous semidirect product	C₉⋊(D₁₁×C₂₃)
unambiguous semidirect product	C₁₁⋊(D₉×C₂₃)

Splittings

Fitting, Hall	C₉×C₁₁×C₂₃ ⋊ C₂
derived, Hall	C₉×C₁₁ ⋊ C₂×C₂₃
Hall	C₁₁×C₂₃ ⋊ D₉
Hall	C₉×C₂₃ ⋊ D₁₁
Sylow	C₁₁ ⋊ D₉×C₂₃
Sylow	C₉ ⋊ D₁₁×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂₃	D₉₉
commutator, cosocle, hypocenter	C₉×C₁₁	C₂×C₂₃
Frattini	C₃	C₂₃×D₃₃
Fitting	C₉×C₁₁×C₂₃	C₂
socle	C₃×C₁₁×C₂₃	D₃
LCS	G ▷ C₉×C₁₁
UCS	C₁ ◁ C₂₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2277

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40,41,42,43);(25,32)(26,31)(27,30)(28,29)(34,43)(35,42)(36,41)(37,40)(38,39)

Conjugacy classes & character table

1173 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₂₃×D₉₉, C₂₃×D₄₉₅, C₂₃×C₉⋊AGL(1,𝔽₁₁), …
maximal normal subgroup of	C₅×C₂₃×D₉₉, C₂₃×C₉⋊AGL(1,𝔽₁₁), C₇×C₂₃×D₉₉
maximal quotient of	C₅×C₂₃×D₉₉, C₂₃×D₄₉₅, C₇×C₂₃×D₉₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4554, 11);

C23×D99 #17986909