Finite Group Databasebeta

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Cayley diagram

C2×C5×#215 #91744

order480
isoclinismisoclinic class of #213
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×C5×#215

Splittings

FittingC2×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ C2×SD16
SylowC3 ⋊ C2×C5×SD16

Subgroups

subgroupG/H
centerC22×C5#67
commutator, cosocleC3×C4C23×C5
FrattiniC4C22×C5×D3
FittingC2×C3×C5×Q8C2
socleC22×C3×C5D4
prime radicalC2×C5×D12C2
hypercenterC2×C5×Q8D3
hypocenterC3C2×C5×SD16
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×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)(6,7,8,9,10)(11,12,14,16)(13,18,17,15);(4,5)(12,15)(13,17)(16,18);(1,2)

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×#215, #11749220, #11749223, …
maximal normal subgroup ofDic5×#215, #11749220, #11749223, …
maximal quotient ofC2×C5×#808, C2×C5×#809, C5×#4968, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 820);