Finite Group Databasebeta

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Cayley diagram

C3×#4034 #91605

order480
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC3×#4034

Splittings

HallC3×C5 ⋊ C4⋊Q8
SylowC5 ⋊ C3×C4⋊Q8

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×C4⋊Q8
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#64873, #11746744, #11747138, …
maximal normal subgroup ofC3×#64873, #11746744, #11747138, …
maximal quotient ofC3×#64935, C3×#64936, C3×#64945, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 681);