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D493 #11758336

order986
isoclinismisoclinic class of D493
automorphismAut(G) order 220864
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD493
unambiguous semidirect productC17⋊D29
unambiguous semidirect productC29⋊D17

Splittings

Fitting, socle, derived, HallC17×C29 ⋊ C2
SylowC29 ⋊ D17
SylowC17 ⋊ D29

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC17×C29C2
LCSG ▷ C17×C29
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 46
transitive degreeμt(G) = 493

A minimal faithful permutation representation — 2 generators on 46 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);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,46)(20,45)(21,44)(22,43)(23,42)(24,41)(25,40)(26,39)(27,38)(28,37)(29,36)(30,35)(31,34)(32,33)

Polycyclic presentation:

2,17,29|b^a=b^16,c^a=c^28

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14520307, #14520308, D17×D29, …
maximal normal subgroup of#14520307, #14520308, D17×D29, …
maximal quotient ofDic493, C2×D493, C3×D493, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(986, 3);