Finite Group Databasebeta

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Cayley diagram

C5×#876 #91679

order480
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#876

Splittings

FittingC3×C42×C5 ⋊ C2
HallC3×C5 ⋊ #126
SylowC3 ⋊ C5×#126

Subgroups

subgroupG/H
centerC22×C5C22×D3
commutator, cosocleC22×C3C23×C5
FrattiniC22C22×C5×D3
FittingC3×C42×C5C2
socleC22×C3×C5C23
prime radicalC22×C5×D3C22
hypercenterC42×C5D3
hypocenterC3C5×#126
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11752567, #11752572, #11752576, …
maximal normal subgroup of#11752567, #11752572, #11752576, …
maximal quotient ofC5×#4658, C5×C3⋊#401, C5×#4675, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 755);