Finite Group Databasebeta

← Prev (#14435423) Next (#14435425) →

C5×#79357 #14435424

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

Aliases

direct productC5×#79357

Splittings

FittingC3×C5×#432 ⋊ C2
HallC3×C5 ⋊ #3117
SylowC3 ⋊ C5×#3117

Subgroups

subgroupG/H
centerC22×C5C22×D12
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#432C2
socleC22×C3×C5C22×D4
prime radicalC5×#930C22
hypercenterC5×#432D3
hypocenterC3C5×#3117
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C5×#432

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 161122);