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D₆₉₅₅ #28358118

• 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 125 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125);(2,5)(3,4)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(20,125)(21,124)(22,123)(23,122)(24,121)(25,120)(26,119)(27,118)(28,117)(29,116)(30,115)(31,114)(32,113)(33,112)(34,111)(35,110)(36,109)(37,108)(38,107)(39,106)(40,105)(41,104)(42,103)(43,102)(44,101)(45,100)(46,99)(47,98)(48,97)(49,96)(50,95)(51,94)(52,93)(53,92)(54,91)(55,90)(56,89)(57,88)(58,87)(59,86)(60,85)(61,84)(62,83)(63,82)(64,81)(65,80)(66,79)(67,78)(68,77)(69,76)(70,75)(71,74)(72,73)

Polycyclic presentation:

2,5,13,107|b^a=b^4,c^a=c^12,d^a=d^106

Conjugacy classes & character table

3479 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13910, 8);