Finite Group Databasebeta

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Cayley diagram

C2×C5×#208 #91724

order480
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×C5×#208

Splittings

HallC3×C5 ⋊ C2×M16
SylowC3 ⋊ C2×C5×M16

Subgroups

subgroupG/H
centerC2×C4×C5C2×D3
commutatorC2×C3C22×C4×C5
FrattiniC4C22×C5×D3
FittingC22×C3×C4×C5C2
socleC22×C3×C5C2×C4
prime radicalC23×C3×C5C4
cosocleC3×C4C23×C5
hypercenterC22×C4×C5D3
hypocenterC3C2×C5×M16
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745970, #11745972, #11745973, …
maximal normal subgroup of#11745970, #11745972, #11745973, …
maximal quotient ofC2×C5×#803, C4×C5×#208, C2×C5×C4⋊(C3⋊C8), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 800);