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#27532702

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 117 points:

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

Polycyclic presentation:

2^8,53|a^2=g,b^2=e,c^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^52,c^b=cg,d^b=def,f^b=fh,d^c=de,e^c=eh,f^c=fh,g^c=gh,e^d=eh,f^d=fh

Conjugacy classes & character table

626 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 318178);