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C5×#71356 #14318028

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#71356

Splittings

FittingC3×C5×#499 ⋊ C2
HallC3×C5 ⋊ #2228
SylowC3 ⋊ C5×#2228

Subgroups

subgroupG/H
centerC22×C5C2×#213
commutator, cosocleC2×C3×C8C23×C5
FrattiniC2×C8C22×C5×D3
FittingC3×C5×#499C2
socleC22×C3×C5C2×D8
prime radicalC2×C5×D24C22
hypercenterC5×#499D3
hypocenterC3C5×#2228
LCSG ▷ C2×C3×C8 ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C4×C5×C8 ◁ C5×#499

272 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

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, 43726);