Finite Group Databasebeta

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Cayley diagram

C2×C3×#677 #91619

order480
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C23×C3 · Schur multiplier (H2) = C22

Aliases

direct productC2×C3×#677

Splittings

FittingC2×C3×C5×C8 ⋊ C2
HallC3×C5 ⋊ C2×SD16
SylowC5 ⋊ C2×C3×SD16

Subgroups

subgroupG/H
centerC22×C3D20
commutator, cosocleC4×C5C23×C3
FrattiniC4C22×C3×D5
FittingC2×C3×C5×C8C2
socleC22×C3×C5D4
prime radicalC2×C3×D20C2
hypercenterC2×C3×C8D5
hypocenterC5C2×C3×SD16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ 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)(11,12,13,15,14,16,17,18);(1,2)(7,8)(9,10)(12,15)(13,17)(16,18);(1,2)

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747749, #11747751, #11747753, …
maximal normal subgroup of#11747749, #11747751, #11747753, …
maximal quotient ofC3×#64969, C3×#64970, C3×C4×#677, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 695);