Finite Group Databasebeta

?

← Prev (#34208384) Next (#34208386) →

#34208385

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

318 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 115 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)(81,83)(84,86,90,101)(85,93,95,110)(87,102,88,106)(89,107,103,100)(91,99,105,98)(92,97,108,109)(94,112,104,115)(96,114,113,111);(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)(82,83)(85,92,95,108)(87,91)(88,105)(89,103)(93,109,110,97)(94,96,104,113)(98,106)(99,102)(100,107)(111,115,114,112);(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)(84,85,91,108,103,113,87,94,90,95,105,92,89,96,88,104)(86,97,106,110,107,112,98,111,101,109,102,93,100,115,99,114)

Polycyclic presentation:

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

Conjugacy classes & character table

1282 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 89684);