Finite Group Databasebeta

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#27303425

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

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

Full subgroup data →

Presentation

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

Polycyclic presentation:

2^8,53|a^2=h,c^2=dg,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^a=i^52,c^b=cf,d^b=dh,e^b=eh,i^b=i^52,d^c=dh,e^c=eg,f^c=fh,g^c=gh,i^c=i^52

Conjugacy classes & character table

866 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 88901);