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Cayley diagram

C3×#4022 #91593

order480
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×#4022

Splittings

FittingC3×C42×C5 ⋊ C2
HallC3×C5 ⋊ #126
SylowC5 ⋊ C3×#126

Subgroups

subgroupG/H
centerC22×C3C22×D5
commutator, cosocleC22×C5C23×C3
FrattiniC22C22×C3×D5
FittingC3×C42×C5C2
socleC22×C3×C5C23
prime radicalC22×C3×D5C22
hypercenterC3×C42D5
hypocenterC5C3×#126
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42

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:

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11752599, #11752602, #11752603, …
maximal normal subgroup of#11752599, #11752602, #11752603, …
maximal quotient ofC3×#64947, C3×C5⋊#401, C3×#64964, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 669);