Finite Group Databasebeta

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C5×#66928 #13183002

order1760
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#66928

Splittings

FittingC42×C5×C11 ⋊ C2
HallC5×C11 ⋊ #124
SylowC11 ⋊ C5×#124

Subgroups

subgroupG/H
centerC22×C5C22×D11
commutator, cosocleC22×C11C23×C5
FrattiniC22C22×C5×D11
FittingC42×C5×C11C2
socleC22×C5×C11C23
prime radicalC2×C5×D44C2
hypercenterC42×C5D11
hypocenterC11C5×#124
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C5 ◁ C42×C5

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 880

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5)(6,7,9,11,13,15,16,14,12,10,8)(17,19,20,18)(22,26)(25,28);(17,18,20,19)(21,23,24,27)(22,25,26,28);(7,8)(9,10)(11,12)(13,14)(15,16)(18,19)(21,22)(23,25)(24,26)(27,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 811);