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Cayley diagram

D73 #3856

order146
isoclinismisoclinic class of D73
automorphismAut(G) = AGL(1,𝔽73) (order 5256) · Inn(G) = G · Out(G) = C4×C9
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD73
unambiguous semidirect productC73⋊C2

Splittings

Fitting, socle, derived, SylowC73 ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC73C2
LCSG ▷ C73
UCSC1

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 73

A minimal faithful permutation representation — 2 generators on 73 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(2,73)(3,72)(4,71)(5,70)(6,69)(7,68)(8,67)(9,66)(10,65)(11,64)(12,63)(13,62)(14,61)(15,60)(16,59)(17,58)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Polycyclic presentation:

2,73|b^a=b^72

Conjugacy classes & character table

38 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#64408, C2×D73, D73⋊C3, …
maximal normal subgroup of#64408, C2×D73, D73⋊C3, …
maximal quotient ofDic73, C2×D73, C3×D73, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(146, 1);