Finite Group Databasebeta

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C5×#68310 #14283064

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#68310

Splittings

HallC3×C5 ⋊ #1506
SylowC3 ⋊ C5×#1506

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#328D3
hypocenterC3C5×#1506
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#328

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

255 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 8762);