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C5×#81679 #14437989

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC5×#81679

Splittings

FittingC3×C5×#489 ⋊ C2
HallC3×C5 ⋊ #3135
SylowC3 ⋊ C5×#3135

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#489C2
socleC22×C3×C5C22×D4
prime radicalC5×#5668C2
hypercenterC5×#489D3
hypocenterC3C5×#3135
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#489

784 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 163687);