Finite Group Databasebeta

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Cayley diagram

C3×#3966 #91036

order480
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC3×#3966

Splittings

HallC3×C5 ⋊ #99
SylowC5 ⋊ C3×#99

Subgroups

subgroupG/H
centerC2×C3C22⋊Dic5
commutatorC22×C5C2×C3×C4
FrattiniC23C2×C3×D5
Fitting, prime radicalC2×C3×C5×D4C2
socleC2×C3×C5C22⋊C4
cosocleC23×C5C22×C3
hypercenterC2×C3×D4D5
hypocenterC5C3×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3 ◁ C23×C3 ◁ C2×C3×D4

104 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)(6,8)(7,10)(9,13)(11,12)(14,15,16);(2,3)(4,5)(6,7)(8,10,13,12)(9,11)

Conjugacy classes & character table

93 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745996, #11745998, #11746002, …
maximal normal subgroup of#11745996, #11745998, #11746002, …
maximal quotient ofC3×#64745, C3×#64746, C3×#64748, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 112);