Finite Group Databasebeta

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C5×#69763 #14298839

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

Aliases

direct productC5×#69763

Splittings

HallC3×C5 ⋊ #1835
SylowC3 ⋊ C5×#1835

Subgroups

subgroupG/H
centerC23×C5C2×D12
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4C23×C5
hypercenterC2×C4×C5×C8D3
hypocenterC3C5×#1835
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 1920

A minimal faithful permutation representation — 3 generators on 36 points:

(1,2,3,4,5)(6,7,8)(14,18)(17,20)(21,24,25,35,27,34,26,23)(22,29,30,28,32,33,31,36);(13,15,16,19)(14,17,18,20)(21,23,26,34,27,35,25,24)(22,28,31,29,32,36,30,33);(7,8)(9,10,11,12)(13,14)(15,17)(16,18)(19,20)(21,22)(23,33)(24,28)(25,31)(26,30)(27,32)(29,35)(34,36)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24537);