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C13×C37⋊C3 #13089648

order1443
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C37⋊C3
unambiguous semidirect productC37⋊(C3×C13)

Splittings

Fitting, socle, HallC13×C37 ⋊ C3
derived, SylowC37 ⋊ C3×C13

Subgroups

subgroupG/H
center, hypercenterC13C37⋊C3
commutator, cosocle, hypocenterC37C3×C13
FrattiniC1G
Fitting, socleC13×C37C3
LCSG ▷ C37
UCSC1 ◁ C13

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 50
transitive degreeμt(G) = 481

A minimal faithful permutation representation — 2 generators on 50 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)(24,29,31)(26,32,28)(30,37,41)(33,39,38)(35,42,36)(40,45,46)(43,47,44)(48,50,49);(14,15,17,21,27,35,43,48,47,32,18,22,28,36,37,20,26,33,40,42,25,31,38,44,45,29,16,19,24,30,34,41,46,49,50,39,23)

Conjugacy classes & character table

195 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13×C37⋊C3, C13×D37⋊C3, D13×C37⋊C3, …
maximal normal subgroup ofC2×C13×C37⋊C3, C13×D37⋊C3, D13×C37⋊C3, …
maximal quotient ofC2×C13×C37⋊C3, C13×#66524, C3×C13×C37⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1443, 2);