Finite Group Databasebeta

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#27304758

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

288 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 121 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)(55,57)(58,61,64,79)(59,66,70,69)(60,72,76,75)(62,77,83,112)(63,78,86,97)(65,88,90,100)(67,91,96,95)(68,92,99,84)(71,101,102,108)(73,103,87,105)(74,104,107,85)(80,109,114,113)(81,110,116,115)(82,111,93,118)(89,98,117,121)(94,106,119,120);(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)(58,60)(59,65)(61,72)(62,81)(63,85)(64,76)(66,88)(67,94)(68,98)(69,100)(70,90)(71,80)(73,82)(74,78)(75,79)(77,110)(83,116)(84,89)(86,104)(87,93)(91,106)(92,117)(95,120)(96,119)(97,107)(99,121)(101,109)(102,114)(103,111)(105,118)(108,113)(112,115);(54,55)(56,57)(58,59,64,70)(60,71,76,102)(61,66,79,69)(62,80,83,114)(63,84,86,92)(65,87,90,73)(67,93,96,82)(68,97,99,78)(72,101,75,108)(74,106,107,120)(77,109,112,113)(81,98,116,121)(85,94,104,119)(88,105,100,103)(89,110,117,115)(91,118,95,111)

Polycyclic presentation:

2^8,53|a^2=h,c^2=h,d^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,d^b=df,f^b=fg,g^b=gh,i^b=i^52,i^c=i^52

Conjugacy classes & character table

1037 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90234);