Finite Group Databasebeta

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Cayley diagram

C2×C3×#688 #91658

order480
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC2×C3×#688

Splittings

FittingC2×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ C2×SD16
SylowC5 ⋊ C2×C3×SD16

Subgroups

subgroupG/H
centerC22×C3C22⋊D5
commutator, cosocleC4×C5C23×C3
FrattiniC4C22×C3×D5
FittingC2×C3×C5×Q8C2
socleC22×C3×C5D4
prime radicalC2×C3×D20C2
hypercenterC2×C3×Q8D5
hypocenterC5C2×C3×SD16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×Q8

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749193, #11749227, #11749228, …
maximal normal subgroup of#11749193, #11749227, #11749228, …
maximal quotient ofC2×C3×#3940, C2×C3×#3941, C3×#65257, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 734);