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C13×D43⋊C3 #16809807

order3354
isoclinismisoclinic class of D43⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D43⋊C3
unambiguous semidirect productD43⋊(C3×C13)
unambiguous semidirect product(C43⋊C3)⋊(C2×C13)

Splittings

Fitting, socle, HallC13×C43 ⋊ C2×C3
derived, SylowC43 ⋊ C2×C3×C13
HallC13×C43⋊C3 ⋊ C2
HallC13×D43 ⋊ C3
HallC43⋊C3 ⋊ C2×C13
HallD43 ⋊ C3×C13

Subgroups

subgroupG/H
center, hypercenterC13D43⋊C3
commutator, cosocle, hypocenterC43C2×C3×C13
FrattiniC1G
Fitting, socleC13×C43C2×C3
LCSG ▷ C43
UCSC1 ◁ C13

16 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)(15,19,20,16,17,21)(18,27,28,22,23,37)(24,40,41,30,31,49)(25,39,35,33,29,26)(32,45,47,36,38,50)(34,51,52,43,42,46)(44,54,55,53,48,56);(14,15,18,24,32,35,20,19,25,34,44,52,28,39,27,38,48,55,41,50,51,40,31,42,47,49,56,54,45,23,29,37,46,53,43,33,17,21,26,36,30,22,16)

Conjugacy classes & character table

169 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13×D43⋊C3, C13×C5⋊(D43⋊C3), C7×C13×D43⋊C3, …
maximal normal subgroup ofC5×C13×D43⋊C3, C7×C13×D43⋊C3, C13×AGL(1,𝔽43), …
maximal quotient ofC5×C13×D43⋊C3, C13×C5⋊(D43⋊C3), C7×C13×D43⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3354, 13);