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C13×C43⋊C7 #16840940

order3913
isoclinismisoclinic class of C43⋊C7
automorphism?
homologyAbelianization (H1) = C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×C43⋊C7
unambiguous semidirect productC43⋊(C7×C13)
unambiguous semidirect product(C13×C43)⋊C7

Splittings

Fitting, socle, HallC13×C43 ⋊ C7
derived, SylowC43 ⋊ C7×C13

Subgroups

subgroupG/H
center, hypercenterC13C43⋊C7
commutator, cosocle, hypocenterC43C7×C13
FrattiniC1G
Fitting, socleC13×C43C7
LCSG ▷ C43
UCSC1 ◁ C13

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 56
transitive degreeμt(G) = 559

A minimal faithful permutation representation — 2 generators on 56 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,16,18,22,27,35,48)(17,20,24,31,42,53,19)(21,26,33,46,23,29,38)(25,30,40,51,34,45,56)(28,37,50,47,36,32,44)(39,49,41,52,43,54,55);(14,15,17,21,18,23,30,41,24,32,45,35,33,47,37,50,27,36,49,46,38,48,53,56,51,44,55,31,43,52,54,40,42,29,39,22,28,26,34,20,25,16,19)

Conjugacy classes & character table

169 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C13×C43⋊C7, C13×(C43⋊C3)⋊C7, C13⋊C3×C43⋊C7, …
maximal normal subgroup ofC3×C13×C43⋊C7, C13×(C43⋊C3)⋊C7, C13⋊C3×C43⋊C7, …
maximal quotient ofC3×C13×C43⋊C7, C5×C13×C43⋊C7, C13×C43⋊C49, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3913, 1);