Finite Group Databasebeta

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Cayley diagram

C3×#3937 #91007

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

Aliases

direct productC3×#3937

Splittings

FittingC3×C42×C5 ⋊ C2
HallC3×C5 ⋊ #104
SylowC5 ⋊ C3×#104

Subgroups

subgroupG/H
centerC3×C4D20
commutatorC4×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
FittingC3×C42×C5C2
socleC2×C3×C5C22⋊C4
prime radicalC3×#709C2
cosocleC2×C4×C5C22×C3
hypercenterC3×C42D5
hypocenterC5C3×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×C42

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 120

A minimal faithful permutation representation — 2 generators on 16 points:

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

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747016, #11747017, #11747106, …
maximal normal subgroup of#11747016, #11747017, #11747106, …
maximal quotient ofC3×#64671, C3×#64672, C3×#64676, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 83);