Finite Group Databasebeta

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Cayley diagram

C2×C3×#676 #91617

order480
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×C3×#676

Splittings

FittingC2×C3×C5×C8 ⋊ C2
HallC3×C5 ⋊ C2×M16
SylowC5 ⋊ C2×C3×M16

Subgroups

subgroupG/H
centerC2×C3×C4C2×D5
commutatorC2×C5C22×C3×C4
FrattiniC4C22×C3×D5
FittingC2×C3×C5×C8C2
socleC22×C3×C5C2×C4
prime radicalC22×C3×D5C4
cosocleC4×C5C23×C3
hypercenterC2×C3×C8D5
hypocenterC5C2×C3×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C2×C3×C8

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:

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745882, C3×#64734, C3×#64891, …
maximal normal subgroup of#11745882, C3×#64734, C3×#64891, …
maximal quotient ofC3×#64968, C3×#64974, C3×C4×#676, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 693);