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D1023 #14523303

order2046
isoclinismisoclinic class of D1023
automorphismAut(G) order 613800
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD1023
unambiguous semidirect productC3⋊D341
unambiguous semidirect productC11⋊D93
unambiguous semidirect productC31⋊D33

Splittings

Fitting, socle, derived, HallC3×C11×C31 ⋊ C2
HallC11×C31 ⋊ D3
HallC3×C31 ⋊ D11
HallC3×C11 ⋊ D31
SylowC31 ⋊ D33
SylowC11 ⋊ D93
SylowC3 ⋊ D341

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C11×C31C2
LCSG ▷ C3×C11×C31
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 1023

A minimal faithful permutation representation — 2 generators on 45 points:

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

Polycyclic presentation:

2,3,11,31|b^a=b^2,c^a=c^10,d^a=d^30

Conjugacy classes & character table

513 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD31×D33, D11×D93, D3×D341, …
maximal normal subgroup ofD31×D33, D11×D93, D3×D341, …
maximal quotient ofDic1023, C2×D1023, C7×D1023, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2046, 9);