Finite Group Databasebeta

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Cayley diagram

C3×#4036 #91607

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

Aliases

direct productC3×#4036

Splittings

HallC3×C5 ⋊ #125
SylowC5 ⋊ C3×#125

Subgroups

subgroupG/H
centerC22×C3C22×D5
commutator, cosocleC22×C5C23×C3
FrattiniC22C22×C3×D5
FittingC3×C5×C4⋊C4C2
socle, prime radicalC22×C3×C5C23
hypercenterC3×C4⋊C4D5
hypocenterC5C3×#125
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 480

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

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#64870, #11746741, #11747142, …
maximal normal subgroup ofC3×#64870, #11746741, #11747142, …
maximal quotient ofC3×#64943, C3×#64944, C3×#64949, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 683);