Finite Group Databasebeta

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C5×#66929 #13183003

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

Aliases

direct productC5×#66929

Splittings

FittingC42×C5×C11 ⋊ C2
HallC5×C11 ⋊ #126
SylowC11 ⋊ C5×#126

Subgroups

subgroupG/H
centerC22×C5C22×D11
commutator, cosocleC22×C11C23×C5
FrattiniC22C22×C5×D11
FittingC42×C5×C11C2
socleC22×C5×C11C23
prime radicalC22×C5×D11C22
hypercenterC42×C5D11
hypocenterC11C5×#126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C5 ◁ C42×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 880

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7,9,11,13,15,16,14,12,10,8)(18,22)(21,24)(25,27,28,32)(26,30,29,31);(17,19,20,23)(18,21,22,24)(26,29)(30,31);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,21)(20,22)(23,24)(25,26)(27,31)(28,29)(30,32)

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, 812);