Finite Group Databasebeta

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Cayley diagram

C3×#3942 #91012

order480
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2

Aliases

direct productC3×#3942

Splittings

HallC3×C5 ⋊ #103
SylowC5 ⋊ C3×#103

Subgroups

subgroupG/H
centerC22×C3C22⋊D5
commutatorC4×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC3×C5×C4⋊C4C2
socle, prime radicalC22×C3×C5D4
cosocleC2×C4×C5C22×C3
hypercenterC3×C4⋊C4D5
hypocenterC5C3×#103
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C3×C4⋊C4

84 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)(6,9,8,7)(11,14)(12,17)(15,16)(18,19,20);(2,3)(4,5)(10,16,13,11)(12,15,17,14)

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747264, #11747265, #11747266, …
maximal normal subgroup of#11747264, #11747265, #11747266, …
maximal quotient ofC3×#64672, C3×#64701, C3×#64704, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 88);