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C5×#71145 #14289583

order1920
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4

Aliases

direct productC5×#71145

Splittings

FittingC3×C5×#476 ⋊ C2
HallC3×C5 ⋊ #1634
SylowC3 ⋊ C5×#1634

Subgroups

subgroupG/H
centerC22×C5#937
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#476C2
socleC22×C3×C5#120
prime radicalC5×#5563C2
hypercenterC5×#476D3
hypocenterC3C5×#1634
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#476

436 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)(6,7,8)(9,10,12,14)(11,16,15,13)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,32,26);(7,8)(11,15)(13,16)(17,19,22,28)(18,23,25,32)(20,27,21,30)(24,31,29,26);(10,13)(11,15)(14,16)(17,18,22,25)(19,26,28,31)(20,24,21,29)(23,30,32,27)

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 15281);