Finite Group Databasebeta

← Prev (#14284122) Next (#14284124) →

C5×#68364 #14284123

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

Aliases

direct productC5×#68364

Splittings

FittingC3×C5×#330 ⋊ C2
HallC3×C5 ⋊ #1529
SylowC3 ⋊ C5×#1529

Subgroups

subgroupG/H
centerC22×C5D3×C22⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#895C4
cosocleC3×C42C23×C5
hypercenterC5×#330D3
hypocenterC3C5×#1529
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#330

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 960

A minimal faithful permutation representation — 3 generators on 32 points:

(1,2,3,4,5)(6,7)(17,20,22,21)(18,24,25,29)(19,27,28,30)(23,31,26,32);(7,8)(9,10)(11,15)(12,14)(13,16)(17,19)(18,23)(20,27)(21,30)(22,28)(24,31)(25,26)(29,32);(10,13,14,15)(17,18,21,24,22,25,20,29)(19,26,27,31,28,23,30,32)

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, 9821);