Finite Group Databasebeta

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Cayley diagram

C3×#3953 #91023

order480
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#3953

Splittings

FittingC2×C3×C5×C8 ⋊ C2
HallC3×C5 ⋊ #102
SylowC5 ⋊ C3×#102

Subgroups

subgroupG/H
centerC22×C3D20
commutatorC4×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC2×C3×C5×C8C2
socleC22×C3×C5D4
prime radicalC2×C3×D20C2
cosocleC2×C4×C5C22×C3
hypercenterC2×C3×C8D5
hypocenterC5C3×#102
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×C8

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 240

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

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747570, #11747571, #11747572, …
maximal normal subgroup of#11747570, #11747571, #11747572, …
maximal quotient ofC3×#64679, C3×#64690, C3×#64705, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 99);