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#34200808

• supersolvable
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

346 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

Full subgroup data →

Presentation

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

(2,9,12,11)(4,19)(8,23,25,24)(10,17,27,28)(13,29,30,26)(14,31)(18,32)(20,21)(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)(2,8)(4,18)(5,15)(6,22)(7,16)(9,23)(10,26)(11,24)(12,25)(13,17)(14,20)(19,32)(21,31)(27,29)(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)(3,13)(4,17)(5,9)(6,11)(7,12)(8,14)(10,20)(15,29)(16,30)(18,23)(19,28)(21,27)(22,26)(24,32)(25,31)(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|c^2=gh,d^2=fh,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fh,g^a=gh,i^a=i^78,d^b=df,e^b=egh,f^b=fh,i^b=i^78,d^c=dg,e^d=eh

Conjugacy classes & character table

1039 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 82107);