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D403 #11717576

order806
isoclinismisoclinic class of D403
automorphismAut(G) order 145080
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD403
unambiguous semidirect productC13⋊D31
unambiguous semidirect productC31⋊D13

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C2
SylowC31 ⋊ D13
SylowC13 ⋊ D31

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C31C2
LCSG ▷ C13×C31
UCSC1

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 403

A minimal faithful permutation representation — 2 generators on 44 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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,44)(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:

2,13,31|b^a=b^12,c^a=c^30

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13×D31, C2×D403, C3×D403, …
maximal normal subgroup ofD13×D31, C2×D403, C3×D403, …
maximal quotient ofDic403, C2×D403, C3×D403, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(806, 3);