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C5×#80298 #14425203

order1920
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC5×#80298

Splittings

FittingC3×C5×#456 ⋊ C2
HallC3×C5 ⋊ #3018
SylowC3 ⋊ C5×#3018

Subgroups

subgroupG/H
centerC2×C5D3×#120
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#456C2
socleC2×C3×C5C2×#120
hypercenterC5×#456D3
hypocenterC3C5×#3018
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#456

1448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 150901);