Finite Group Databasebeta

← Prev (#11755967) Next (#11755969) →

C5×#5583 #11755968

order960
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#5583

Splittings

FittingC3×C4×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #541
SylowC3 ⋊ C5×#541

Subgroups

subgroupG/H
centerC22×C5C23×D3
commutator, cosocleC22×C3C24×C5
FrattiniC22C23×C5×D3
FittingC3×C4×C5×Q8C2
socleC22×C3×C5C24
prime radicalC22×C5×D3C23
hypercenterC4×C5×Q8D3
hypocenterC3C5×#541
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C4×C5×Q8

384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×#79657, C5×#79849, C5×#79786, …
maximal normal subgroup ofC5×#79657, C5×#79849, C5×#79786, …
maximal quotient ofC5×#73760, C5×#73625, C5×#82454, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 10163);