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C5×#69026 #14298658

order1920
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC5×#69026

Splittings

FittingC3×C5×#344 ⋊ C2
HallC3×C5 ⋊ #1829
SylowC3 ⋊ C5×#1829

Subgroups

subgroupG/H
centerC2×C5#4664
commutatorC23×C3C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#344C2
socleC2×C3×C5#381
prime radicalC22×C5×D12C22
cosocleC22×C3×C4C23×C5
hypercenterC5×#344D3
hypocenterC3C5×#1829
LCSG ▷ C23×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#344

544 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)(6,7,8)(9,11)(10,15,14,17)(12,19)(13,18)(16,23,21,24)(20,22);(7,8)(10,14)(12,20)(15,17)(19,22);(9,10,12,16,13,14,20,21)(11,17,19,24,18,15,22,23)

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, 24356);