Finite Group Databasebeta

← Prev (#14424662) Next (#14424664) →

C5×#80231 #14424663

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

Aliases

direct productC5×#80231

Splittings

FittingC3×C5×#452 ⋊ C2
HallC3×C5 ⋊ #3012
SylowC3 ⋊ C5×#3012

Subgroups

subgroupG/H
centerC22×C5C2×D3×D4
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#452C2
socleC22×C3×C5C22×D4
hypercenterC5×#452D3
hypocenterC3C5×#3012
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#452

1528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 28
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 4 generators on 28 points:

(1,2,3,4,5)(6,7)(13,15,17,22)(14,19,21,26)(16,23,24,28)(18,25,20,27);(10,12)(15,22)(19,26)(23,28)(25,27);(7,8)(14,18)(16,24)(19,25)(20,21)(23,28)(26,27);(7,8)(9,10)(11,12)(13,14)(15,19)(16,18)(17,21)(20,24)(22,26)(23,25)(27,28)

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, 150361);