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D989 #14520373

order1978
isoclinismisoclinic class of D989
automorphismAut(G) order 913836
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD989
unambiguous semidirect productC23⋊D43
unambiguous semidirect productC43⋊D23

Splittings

Fitting, socle, derived, HallC23×C43 ⋊ C2
SylowC43 ⋊ D23
SylowC23 ⋊ D43

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC23×C43C2
LCSG ▷ C23×C43
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 66
transitive degreeμt(G) = 989

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Polycyclic presentation:

2,23,43|b^a=b^22,c^a=c^42

Conjugacy classes & character table

496 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD23×D43, C2×D989, C7×D989, …
maximal normal subgroup ofD23×D43, C2×D989, C7×D989, …
maximal quotient ofDic989, C2×D989, C7×D989, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1978, 3);