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C13×C31⋊C3 #11925880

order1209
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C31⋊C3
unambiguous semidirect productC31⋊(C3×C13)

Splittings

Fitting, socle, HallC13×C31 ⋊ C3
derived, SylowC31 ⋊ C3×C13

Subgroups

subgroupG/H
center, hypercenterC13C31⋊C3
commutator, cosocle, hypocenterC31C3×C13
FrattiniC1G
Fitting, socleC13×C31C3
LCSG ▷ C31
UCSC1 ◁ C13

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 403

A minimal faithful permutation representation — 2 generators on 44 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16,18)(17,20,25)(19,23,22)(21,27,34)(24,30,32)(26,28,29)(31,37,41)(33,38,39)(35,42,36)(40,43,44);(14,15,17,21,28,18,22,29,36,42,25,32,39,27,35,34,41,44,37,20,26,33,40,43,30,16,19,24,31,38,23)

Conjugacy classes & character table

169 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13×C31⋊C3, C13×D31⋊C3, D13×C31⋊C3, …
maximal normal subgroup ofC2×C13×C31⋊C3, C13×D31⋊C3, D13×C31⋊C3, …
maximal quotient ofC2×C13×C31⋊C3, C13×C31⋊C9, C3×C13×C31⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1209, 2);