Finite Group Databasebeta

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#34201630

• supersolvable
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

286 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:

(1,3,6,15)(2,9)(4,19,20,14)(5,16,7,23)(8,24)(10,25)(11,26)(12,13)(17,28)(18,32,21,31)(22,30)(27,29)(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);(2,8)(4,18)(5,7)(9,24)(10,22)(11,27)(12,17)(13,28)(14,31)(16,23)(19,32)(20,21)(25,30)(26,29)(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);(1,2,7,11,6,12,5,22)(3,13,23,30,15,9,16,26)(4,17,18,27,20,8,21,10)(14,24,31,25,19,28,32,29)(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=fg,c^2=g,d^2=f,f^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fh,g^a=gh,i^a=i^78,d^b=dfh,e^b=egh,f^b=fh,i^b=i^78,d^c=dg,e^c=eh,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, 82929);