Finite Group Databasebeta

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Cayley diagram

C5×#953 #91756

order480
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C24

Aliases

direct productC5×#953

Splittings

FittingC24×C3×C5 ⋊ C2
HallC3×C5 ⋊ #120
SylowC3 ⋊ C5×#120

Subgroups

subgroupG/H
centerC22×C5C22×D3
commutator, cosocleC22×C3C23×C5
FrattiniC22C22×C5×D3
FittingC24×C3×C5C2
socleC22×C3×C5C23
hypercenterC24×C5D3
hypocenterC3C5×#120
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C24×C5

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 3 generators on 16 points:

(1,2,3)(5,7)(12,13,14,15,16);(9,11);(2,3)(4,5)(6,7)(8,9)(10,11)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749525, C5×#5032, #11755381, …
maximal normal subgroup of#11749525, C5×#5032, #11755381, …
maximal quotient ofC5×#5210, C5×#5213, C5×#5217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 832);