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#34184404

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

428 conjugacy classes of subgroups; only the 97 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)(82,90)(86,94)(89,95)(91,92)(96,98)(97,102)(99,107)(100,105)(101,109)(103,111)(104,108)(106,110);(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)(80,82,85,90)(81,86)(83,91,84,92)(87,89)(88,94)(93,95)(96,97,99,106,100,103,108,101)(98,102,107,110,105,111,104,109);(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)(80,81,84,87,85,88,83,93)(82,89,92,94,90,95,91,86)(97,101,103,106)(98,104,105,107)

Polycyclic presentation:

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

Conjugacy classes & character table

1762 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 65703);