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C₅×#63140 #13050351

order	1320
isoclinism	isoclinic class of #63140
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Hall	C₃×C₅×C₁₁ ⋊ D₄
Hall	C₅×C₁₁ ⋊ #67
Hall	C₃×C₁₁ ⋊ C₅×D₄
Hall	C₃×C₅ ⋊ C₂²⋊D₁₁
Sylow	C₁₁ ⋊ C₅×#67
Sylow	C₃ ⋊ C₅×C₂²⋊D₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₃×D₁₁
commutator, cosocle	C₂×C₃×C₁₁	C₂²×C₅
Frattini	C₂	C₅×D₃×D₁₁
Fitting, socle	C₂×C₃×C₅×C₁₁	C₂²
hypocenter	C₃×C₁₁	C₅×D₄
LCS	G ▷ C₂×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂×C₅

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 660

A minimal faithful permutation representation — 2 generators on 23 points:

(1,2,3,4,5)(6,7,9,11,13,15,16,14,12,10,8)(18,19)(21,23);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18,19)(20,21)(22,23)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 55);