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C5×#70327 #14297315

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#70327

Splittings

FittingC3×C5×#418 ⋊ C2
HallC3×C5 ⋊ #1795
SylowC3 ⋊ C5×#1795

Subgroups

subgroupG/H
centerC2×C5#4955
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#418C2
socleC2×C3×C5#379
prime radicalC2×C5×#1004C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#418D3
hypocenterC3C5×#1795
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#418

1176 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)(7,8)(9,11)(10,15)(12,19)(13,20)(14,22)(16,23)(17,18)(21,24);(6,7,8)(10,14)(12,21)(15,22)(16,17)(18,23)(19,24);(9,10)(11,18,20,15)(12,14)(13,17)(16,21)(19,23,24,22)

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, 23013);