Finite Group Databasebeta

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C5×#69483 #14303228

order1920
isoclinismisoclinic class of #4656
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#69483

Splittings

HallC3×C5 ⋊ #1917
SylowC3 ⋊ C5×#1917

Subgroups

subgroupG/H
centerC22×C4×C5C22×D3
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C4×C5×C4⋊C4C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4C23×C5
hypercenterC4×C5×C4⋊C4D3
hypocenterC3C5×#1917
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4×C5 ◁ C4×C5×C4⋊C4

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 1920

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

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 28926);