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Cayley diagram

C5×D31 #64581

order310
isoclinismisoclinic class of D31
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D31

Splittings

Fitting, socle, HallC5×C31 ⋊ C2
derived, SylowC31 ⋊ C2×C5

Subgroups

subgroupG/H
center, hypercenterC5D31
commutator, cosocle, hypocenterC31C2×C5
FrattiniC1G
Fitting, socleC5×C31C2
LCSG ▷ C31
UCSC1 ◁ C5

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 36
transitive degreeμt(G) = 155

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36);(6,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,36,34,32,30,28,26,24,22,20,18,16,14,12,10,8)

Conjugacy classes & character table

85 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×D31, C2×C5×D31, C5×D31⋊C3, …
maximal normal subgroup ofD5×D31, C2×C5×D31, C5×D31⋊C3, …
maximal quotient ofC5×Dic31, C2×C5×D31, C3×C5×D31, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(310, 4);