Finite Group Databasebeta

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#27158525

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

364 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 121 points:

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

Polycyclic presentation:

2^7,97|a^2=f,b^2=e,c^2=ef,f^2=g,b^a=be,d^a=dg,h^a=h^75,h^c=h^22,h^d=h^96,h^f=h^96

Conjugacy classes & character table

392 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 21299);