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Cayley diagram

C5×C31⋊C3 #90821

order465
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C31⋊C3
unambiguous semidirect product(C5×C31)⋊C3

Splittings

Fitting, socle, HallC5×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC5C31⋊C3
commutator, cosocle, hypocenterC31C3×C5
FrattiniC1G
Fitting, socleC5×C31C3
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)(7,8,10)(9,12,17)(11,15,14)(13,19,26)(16,22,24)(18,20,21)(23,29,33)(25,30,31)(27,34,28)(32,35,36);(6,7,9,13,20,10,14,21,28,34,17,24,31,19,27,26,33,36,29,12,18,25,32,35,22,8,11,16,23,30,15)

Conjugacy classes & character table

65 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D31⋊C3, D5×C31⋊C3, C5⋊(D31⋊C3), …
maximal normal subgroup ofC5×D31⋊C3, D5×C31⋊C3, C5⋊(D31⋊C3), …
maximal quotient ofC2×C5×C31⋊C3, C5×C31⋊C9, C3×C5×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(465, 3);