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C5×#81013 #14430918

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

Aliases

direct productC5×#81013

Splittings

FittingC3×C5×#475 ⋊ C2
HallC3×C5 ⋊ #3082
SylowC3 ⋊ C5×#3082

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#475C2
socleC22×C3×C5C22×D4
prime radicalC22×C5×D3C2×D4
hypercenterC5×#475D3
hypocenterC3C5×#3082
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#475

724 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)(18,23)(22,30)(24,31)(29,32);(6,7,8)(17,19,21,26)(18,22,23,30)(20,28,27,25)(24,32,31,29);(9,11,12,16)(10,13,14,15)(17,18)(19,22)(20,24)(21,23)(25,29)(26,30)(27,31)(28,32);(9,10,12,14)(11,15,16,13)(19,25)(20,27)(22,29)(24,31)(26,28)(30,32)

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, 156616);