Finite Group Databasebeta

← Prev (#13050346) Next (#13050348) →

C₃×#89170 #13050347

order	1320
isoclinism	isoclinic class of #89167
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₁

Aliases

Splittings

Hall	C₃×C₅×C₁₁ ⋊ Q₈
Hall	C₅×C₁₁ ⋊ C₃×Q₈
Hall	C₃×C₁₁ ⋊ Dic₁₀
Hall	C₃×C₅ ⋊ Dic₂₂
Sylow	C₁₁ ⋊ C₃×Dic₁₀
Sylow	C₅ ⋊ C₃×Dic₂₂

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₅×D₁₁
commutator, cosocle	C₂×C₅×C₁₁	C₂²×C₃
Frattini	C₂	C₃×D₅×D₁₁
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₁	C₂²
hypocenter	C₅×C₁₁	C₃×Q₈
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂×C₃

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 1320

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3)(4,5,7,9,11,13,14,12,10,8,6)(16,17)(18,19)(20,22,23,27)(21,24,25,26);(5,6)(7,8)(9,10)(11,12)(13,14)(15,16,18,19,17)(20,21,23,25)(22,26,27,24)

Conjugacy classes & character table

159 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1320, 51);