Finite Group Databasebeta

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C₁₃×#686 #11760134

order	1040
isoclinism	isoclinic class of #686
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

Splittings

Fitting	C₅×D₄×C₁₃ ⋊ C₂
Hall	C₅×C₁₃ ⋊ D₈
Sylow	C₅ ⋊ C₁₃×D₈

Subgroups

	subgroup	G/H
center	C₂×C₁₃	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂²×C₁₃
Frattini	C₄	C₂×D₅×C₁₃
Fitting	C₅×D₄×C₁₃	C₂
socle	C₂×C₅×C₁₃	D₄
hypercenter	D₄×C₁₃	D₅
hypocenter	C₅	C₁₃×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ D₄×C₁₃

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 520

A minimal faithful permutation representation — 2 generators on 26 points:

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

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1040, 63);