Finite Group Databasebeta

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Cayley diagram

C3×#3947 #91017

order480
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C3×C42 · Schur multiplier (H2) = C2

Aliases

direct productC3×#3947

Splittings

HallC3×C5 ⋊ #97
SylowC5 ⋊ C3×#97

Subgroups

subgroupG/H
centerC2×C3×C4C2×D5
commutatorC2×C5C3×C42
FrattiniC2×C4C2×C3×D5
FittingC2×C3×C5×C8C2
socle, prime radicalC22×C3×C5C2×C4
cosocleC2×C4×C5C22×C3
hypercenterC2×C3×C8D5
hypocenterC5C3×#97
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C8

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 20 points:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745876, C3×#64732, C3×#64890, …
maximal normal subgroup of#11745876, C3×#64732, C3×#64890, …
maximal quotient ofC3×#64674, C3×#64675, C3×#64732, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 93);