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Dic₉₇ #87602

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 101 points:

(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101);(1,3,2,4)(6,101)(7,100)(8,99)(9,98)(10,97)(11,96)(12,95)(13,94)(14,93)(15,92)(16,91)(17,90)(18,89)(19,88)(20,87)(21,86)(22,85)(23,84)(24,83)(25,82)(26,81)(27,80)(28,79)(29,78)(30,77)(31,76)(32,75)(33,74)(34,73)(35,72)(36,71)(37,70)(38,69)(39,68)(40,67)(41,66)(42,65)(43,64)(44,63)(45,62)(46,61)(47,60)(48,59)(49,58)(50,57)(51,56)(52,55)(53,54)

Polycyclic presentation:

2^2,97|a^2=b,c^a=c^96

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(388, 1);