Finite Group Databasebeta

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Cayley diagram

C3×#4099 #91670

order480
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C24

Aliases

direct productC3×#4099

Splittings

FittingC24×C3×C5 ⋊ C2
HallC3×C5 ⋊ #120
SylowC5 ⋊ C3×#120

Subgroups

subgroupG/H
centerC22×C3C22×D5
commutator, cosocleC22×C5C23×C3
FrattiniC22C22×C3×D5
FittingC24×C3×C5C2
socleC22×C3×C5C23
hypercenterC24×C3D5
hypocenterC5C3×#120
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C24×C3

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:

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#64934, #11746805, #11749525, …
maximal normal subgroup ofC3×#64934, #11746805, #11749525, …
maximal quotient ofC3×#65499, C3×#65502, C3×#65506, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 746);