Finite Group Databasebeta

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Cayley diagram

C2×#6706 #91791

order480
isoclinismisoclinic class of #6706
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#6706

Splittings

FittingC2×C3×C5×C8 ⋊ C2
HallC3×C5 ⋊ C2×SD16
SylowC5 ⋊ C2×#204
SylowC3 ⋊ C2×#677

Subgroups

subgroupG/H
centerC22D60
commutator, cosocleC3×C4×C5C23
FrattiniC4C22×D15
FittingC2×C3×C5×C8C2
socleC22×C3×C5D4
prime radicalC2×D60C2
hypercenterC2×C8D15
hypocenterC3×C5C2×SD16
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×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)(4,5)(7,8)(9,10)(12,15)(13,17)(16,18);(1,2)

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747760, #11747761, #11747778, …
maximal normal subgroup of#11747760, #11747761, #11747778, …
maximal quotient of#11750781, #11750782, C4×#6706, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 867);