Finite Group Databasebeta

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C5×#69600 #14303308

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

Aliases

direct productC5×#69600

Splittings

HallC3×C5 ⋊ #1918
SylowC3 ⋊ C5×#1918

Subgroups

subgroupG/H
centerC23×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#389C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#389D3
hypocenterC3C5×#1918
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C5×#389

460 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)(7,8)(13,15,16,19)(14,18,17,20)(22,25)(23,28)(26,27);(6,7,8)(9,11,12,10)(14,17)(18,20);(9,10,12,11)(13,14)(15,18)(16,17)(19,20)(21,22)(23,25)(24,27)(26,28)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 29006);