Finite Group Databasebeta

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#34206625

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

448 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 111 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)(80,83,85,88,87,102,86,101)(81,89,91,96,92,107,104,111)(82,95,97,106,99,90,98,109)(84,100,94,93,103,110,105,108);(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)(80,82,94,107)(81,88,106,110)(83,95,93,104)(84,96,86,98)(85,97,103,111)(87,99,105,89)(90,108,91,102)(92,101,109,100);(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)(80,81,86,91,87,92,85,104)(82,93,98,110,99,108,97,100)(83,96,101,107,102,111,88,89)(84,90,94,106,103,95,105,109)

Polycyclic presentation:

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

Conjugacy classes & character table

931 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 87924);