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#34207323

• supersolvable
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

686 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 111 points:

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

Polycyclic presentation:

2^8,79|a^2=h,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,f^a=fgh,i^a=i^78,c^b=cf,d^b=dh,f^b=fh,g^b=gh,i^b=i^78,d^c=dg,e^c=eh,f^c=fh,f^d=fh

Conjugacy classes & character table

925 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 88622);