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#34207662

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

436 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 115 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)(81,83)(84,87,88,102,91,104,90,108)(85,93,94,110,97,111,96,101)(86,98,99,113,100,114,95,112)(89,106,105,103,107,115,92,109);(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)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(84,86,91,100)(85,92,97,105)(87,101,104,110)(88,95,90,99)(89,94,107,96)(93,102,111,108)(98,109,114,103)(106,113,115,112);(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)(84,85,91,97)(86,89,100,107)(87,98,104,114)(88,96,90,94)(92,95,105,99)(93,109,111,103)(101,106,110,115)(102,112,108,113)

Polycyclic presentation:

2^8,79|a^2=h,b^2=h,c^2=d,d^2=h,e^2=gh,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,f^a=fg,g^a=gh,i^a=i^78,c^b=cf,d^b=dh,e^b=eg,f^b=fg,g^b=gh,i^b=i^78,e^c=egh,f^c=fgh,g^c=gh,i^c=i^78

Conjugacy classes & character table

2224 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 88961);