Finite Group Databasebeta

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Cayley diagram

C5×#805 #91048

order480
isoclinismisoclinic class of #204
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×#805

Splittings

FittingC3×C42×C5 ⋊ C2
HallC3×C5 ⋊ #104
SylowC3 ⋊ C5×#104

Subgroups

subgroupG/H
centerC4×C5D12
commutatorC3×C4C2×C4×C5
FrattiniC2×C4C2×C5×D3
FittingC3×C42×C5C2
socleC2×C3×C5C22⋊C4
prime radicalC5×#235C2
cosocleC2×C3×C4C22×C5
hypercenterC42×C5D3
hypocenterC3C5×#104
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C42×C5

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:

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

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747018, #11747019, #11747106, …
maximal normal subgroup of#11747018, #11747019, #11747106, …
maximal quotient ofC5×#4451, C5×#4452, C5×#4456, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 124);