Finite Group Databasebeta

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#27157500

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 117 points:

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

Polycyclic presentation:

2^7,97|a^2=e,b^2=f,c^2=e,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^96,c^b=cg,h^b=h^22,h^f=h^96

Conjugacy classes & character table

524 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 20274);