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C5×#68284 #14287684

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

Aliases

direct productC5×#68284

Splittings

FittingC3×C5×#327 ⋊ C2
HallC3×C5 ⋊ #1595
SylowC3 ⋊ C5×#1595

Subgroups

subgroupG/H
centerC22×C5#882
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#327C2
socleC22×C3×C5#120
hypercenterC5×#327D3
hypocenterC3C5×#1595
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#327

736 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7)(9,11)(10,13)(12,15)(14,16);(9,10)(11,13)(12,14)(15,16)(18,21)(19,24)(22,23);(7,8)(13,16)(17,18)(19,21)(20,23)(22,24)

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, 13382);