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D957 #14274286

order1914
isoclinismisoclinic class of D957
automorphismAut(G) order 535920
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD957
unambiguous semidirect productC3⋊D319
unambiguous semidirect productC11⋊D87
unambiguous semidirect productC29⋊D33

Splittings

Fitting, socle, derived, HallC3×C11×C29 ⋊ C2
HallC11×C29 ⋊ D3
HallC3×C29 ⋊ D11
HallC3×C11 ⋊ D29
SylowC29 ⋊ D33
SylowC11 ⋊ D87
SylowC3 ⋊ D319

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C29C2
LCSG ▷ C3×C11×C29
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 43
transitive degreeμt(G) = 957

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14)(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);(2,3)(5,14)(6,13)(7,12)(8,11)(9,10)(16,43)(17,42)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Polycyclic presentation:

2,3,11,29|b^a=b^2,c^a=c^10,d^a=d^28

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD29×D33, D11×D87, D3×D319, …
maximal normal subgroup ofD29×D33, D11×D87, D3×D319, …
maximal quotient ofDic957, C2×D957, C7×D957, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1914, 7);