Finite Group Databasebeta

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Cayley diagram

C3×#3950 #91020

order480
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#3950

Splittings

HallC3×C5 ⋊ #107
SylowC5 ⋊ C3×#107

Subgroups

subgroupG/H
centerC22×C3D20
commutatorC4×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC2×C3×C5×C8C2
socle, prime radicalC22×C3×C5D4
cosocleC2×C4×C5C22×C3
hypercenterC2×C3×C8D5
hypocenterC5C3×#107
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

72 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)(10,17,12,11,13,14,15,16)(18,19,20);(2,3)(4,5)(6,9,8,7)(11,14)(12,15)(16,17)

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745893, #11745895, #11745899, …
maximal normal subgroup of#11745893, #11745895, #11745899, …
maximal quotient ofC3×#64678, C3×#64724, C3×#64725, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 96);