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C31×C13⋊C3 #11925879

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

Aliases

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

Splittings

Fitting, socle, HallC13×C31 ⋊ C3
derived, SylowC13 ⋊ C3×C31

Subgroups

subgroupG/H
center, hypercenterC31C13⋊C3
commutator, cosocle, hypocenterC13C3×C31
FrattiniC1G
Fitting, socleC13×C31C3
LCSG ▷ C13
UCSC1 ◁ C31

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:

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

Conjugacy classes & character table

217 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1209, 1);