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C5×#68327 #14288146

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

Aliases

direct productC5×#68327

Splittings

HallC3×C5 ⋊ #1605
SylowC3 ⋊ C5×#1605

Subgroups

subgroupG/H
centerC22×C5#882
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#328C2
socleC22×C3×C5#120
prime radicalC23×C3×C5C2×D4
hypercenterC5×#328D3
hypocenterC3C5×#1605
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#328

476 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 13844);