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Cayley diagram

D97 #5986

order194
isoclinismisoclinic class of D97
automorphismAut(G) = AGL(1,𝔽97) (order 9312) · Inn(G) = G · Out(G) = C3×C16
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C1

Aliases

dihedralD97
unambiguous semidirect productC97⋊C2

Splittings

Fitting, socle, derived, SylowC97 ⋊ C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC97C2
LCSG ▷ C97
UCSC1

4 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 97
transitive degreeμt(G) = 97

A minimal faithful permutation representation — 2 generators on 97 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97);(2,97)(3,96)(4,95)(5,94)(6,93)(7,92)(8,91)(9,90)(10,89)(11,88)(12,87)(13,86)(14,85)(15,84)(16,83)(17,82)(18,81)(19,80)(20,79)(21,78)(22,77)(23,76)(24,75)(25,74)(26,73)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)

Polycyclic presentation:

2,97|b^a=b^96

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#87604, C2×D97, D97⋊C3, …
maximal normal subgroup of#87604, C2×D97, D97⋊C3, …
maximal quotient ofDic97, C2×D97, C3×D97, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(194, 1);