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D667 #13050671

order1334
isoclinismisoclinic class of D667
automorphismAut(G) order 410872
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD667
unambiguous semidirect productC23⋊D29
unambiguous semidirect productC29⋊D23

Splittings

Fitting, socle, derived, HallC23×C29 ⋊ C2
SylowC29 ⋊ D23
SylowC23 ⋊ D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC23×C29C2
LCSG ▷ C23×C29
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 52
transitive degreeμt(G) = 667

A minimal faithful permutation representation — 2 generators on 52 points:

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

Polycyclic presentation:

2,23,29|b^a=b^22,c^a=c^28

Conjugacy classes & character table

335 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD23×D29, C2×D667, C3×D667, …
maximal normal subgroup ofD23×D29, C2×D667, C3×D667, …
maximal quotient ofDic667, C2×D667, C3×D667, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1334, 3);