Finite Group Databasebeta

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Cayley diagram

C5×#907 #91710

order480
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×#907

Splittings

FittingC3×C5×M16 ⋊ C2
HallC3×C5 ⋊ #131
SylowC3 ⋊ C5×#131

Subgroups

subgroupG/H
centerC4×C5C22×D3
commutatorC2×C3C22×C4×C5
FrattiniC4C22×C5×D3
FittingC3×C5×M16C2
socleC2×C3×C5C22×C4
prime radicalC5×#235C2
cosocleC3×C4C23×C5
hypercenterC5×M16D3
hypocenterC3C5×#131
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C5×M16

124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 24
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3)(4,12,7,18,8,6,14,13)(5,15,11,19,9,10,16,17)(20,21,22,23,24);(5,9)(6,12)(11,16)(13,18);(2,3)(4,5)(6,10)(7,11)(8,9)(12,15)(13,17)(14,16)(18,19)

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11748204, #11748205, #11748208, …
maximal normal subgroup of#11748204, #11748205, #11748208, …
maximal quotient ofC5×#4701, C5×#4706, C5×#4708, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 786);