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C13⋊C3×D43 #16809808

order3354
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×D43

Splittings

Fitting, socle, derived, HallC13×C43 ⋊ C2×C3
HallC13⋊C3×C43 ⋊ C2
HallC13×D43 ⋊ C3
SylowC43 ⋊ C2×C13⋊C3
SylowC13 ⋊ C3×D43

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C43C2×C3
LCSG ▷ C13×C43
UCSC1

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:

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

Conjugacy classes & character table

161 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×D43, C13⋊C3×D215, C7×C13⋊C3×D43, …
maximal normal subgroup ofC5×C13⋊C3×D43, C7×C13⋊C3×D43, C13⋊C3×D43⋊C7, …
maximal quotient ofC5×C13⋊C3×D43, C13⋊C3×D215, C7×C13⋊C3×D43, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3354, 14);