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D₇₈₆₉ #30628676

• metacyclic
• supersolvable
• metabelian
• solvable
• monomial
• stem
• Frobenius

Aliases

Splittings

Subgroups

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 107 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)(47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107);(2,3)(5,46)(6,45)(7,44)(8,43)(9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(48,107)(49,106)(50,105)(51,104)(52,103)(53,102)(54,101)(55,100)(56,99)(57,98)(58,97)(59,96)(60,95)(61,94)(62,93)(63,92)(64,91)(65,90)(66,89)(67,88)(68,87)(69,86)(70,85)(71,84)(72,83)(73,82)(74,81)(75,80)(76,79)(77,78)

Polycyclic presentation:

2,3,43,61|b^a=b^2,c^a=c^42,d^a=d^60

Conjugacy classes & character table

3936 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15738, 12);