Finite Group Databasebeta

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Cayley diagram

C3×#4093 #91664

order480
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C2×C4

Aliases

direct productC3×#4093

Splittings

FittingC2×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ #124
SylowC5 ⋊ C3×#124

Subgroups

subgroupG/H
centerC22×C3C22×D5
commutator, cosocleC22×C5C23×C3
FrattiniC22C22×C3×D5
FittingC2×C3×C5×Q8C2
socleC22×C3×C5C23
prime radicalC2×C3×D20C2
hypercenterC2×C3×Q8D5
hypocenterC5C3×#124
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×Q8

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746012, C3×#64697, C3×#64927, …
maximal normal subgroup of#11746012, C3×#64697, C3×#64927, …
maximal quotient ofC3×#65266, C3×#65275, C3×#65277, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 740);