Finite Group Databasebeta

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C5×#75828 #14323534

order1920
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×#75828

Splittings

FittingC3×C5×#388 ⋊ C2
HallC3×C5 ⋊ #2322
SylowC3 ⋊ C5×#2322

Subgroups

subgroupG/H
centerC23×C5C23×D3
commutatorC22×C3C23×C4×C5
FrattiniC23C23×C5×D3
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC22×C5×#67C22
cosocleC23×C3C24×C5
hypercenterC5×#388D3
hypocenterC3C5×#2322
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C5×#388

1264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 960

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

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

Conjugacy classes & character table

360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 49232);