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C3⋊(C17⋊(D43⋊C3)) #27190485

order13158
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C17⋊(D43⋊C3))
unambiguous semidirect productC17⋊(C3⋊(D43⋊C3))
unambiguous semidirect product(C43⋊C3)⋊D51
unambiguous semidirect productD2193⋊C3

Splittings

Fitting, socle, derivedC3×C17×C43 ⋊ C2×C3
HallC3×C17×C43⋊C3 ⋊ C2
HallC17×C43 ⋊ C3×D3
HallC3×C43⋊C3 ⋊ D17
SylowC43 ⋊ C3×D51
SylowC17 ⋊ C3⋊(D43⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C17×C43C2×C3
LCSG ▷ C3×C17×C43
UCSC1

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 2193

A minimal faithful permutation representation — 2 generators on 63 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,36)(12,26,22,20,16,13)(19,32,34,23,25,37)(21,38,39,30,29,33)(31,41,42,40,35,43)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(62,63);(1,2,5,11,19,22,7,6,12,21,31,39,15,26,14,25,35,42,28,37,38,27,18,29,34,36,43,41,32,10,16,24,33,40,30,20,4,8,13,23,17,9,3)(44,45,47,49,51,53,55,57,59,60,58,56,54,52,50,48,46)(61,62,63)

Polycyclic presentation:

2,3^2,17,43|c^a=c^2,d^a=d^16,e^a=e^42,e^b=e^36

Conjugacy classes & character table

438 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD51×D43⋊C3, D17×C3⋊(D43⋊C3), D3×C17⋊(D43⋊C3), …
maximal normal subgroup ofD51×D43⋊C3, D17×C3⋊(D43⋊C3), D3×C17⋊(D43⋊C3), …
maximal quotient ofC3⋊((C43⋊C3)⋊Dic17), C2×C3⋊(C17⋊(D43⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13158, 19);