Finite Group Databasebeta

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#27186879

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 113 points:

(1,2)(3,5)(4,11)(6,7)(8,10)(9,24)(12,14)(13,20)(15,16)(17,19)(18,41)(21,23)(22,37)(25,27)(26,33)(28,29)(30,32)(31,62)(34,36)(35,58)(38,40)(39,54)(42,44)(43,50)(45,46)(47,49)(48,80)(51,53)(52,77)(55,57)(56,73)(59,61)(60,69)(63,64)(66,68)(67,91)(70,72)(71,88)(74,76)(75,84)(78,79)(81,83)(82,98)(85,87)(86,95)(89,90)(92,94)(93,101)(96,97)(99,100)(102,104,105,103);(2,4,3,6)(5,9,8,15)(7,13,12,11)(10,18,17,28)(14,22,21,24)(16,26,25,20)(19,31,30,45)(23,35,34,41)(27,39,38,37)(29,43,42,33)(32,48,47,65)(36,52,51,62)(40,56,55,58)(44,60,59,54)(46,49,63,50)(53,67,66,80)(57,71,70,77)(61,75,74,73)(64,68,78,69)(72,82,81,91)(76,86,85,88)(79,83,89,84)(87,93,92,98)(90,94,96,95)(97,100,99,101)(106,108)(107,110,111,112)(109,113);(2,3)(4,6)(5,8)(7,12)(9,15)(10,17)(11,13)(14,21)(16,25)(18,28)(19,30)(20,26)(22,24)(23,34)(27,38)(29,42)(31,45)(32,47)(33,43)(35,41)(36,51)(37,39)(40,55)(44,59)(46,63)(48,65)(49,50)(52,62)(53,66)(54,60)(56,58)(57,70)(61,74)(64,78)(67,80)(68,69)(71,77)(72,81)(73,75)(76,85)(79,89)(82,91)(83,84)(86,88)(87,92)(90,96)(93,98)(94,95)(97,99)(100,101)(102,103,105,104)(106,107)(108,112)(109,111)(110,113)

Polycyclic presentation:

2^7,101|a^2=e,b^2=f,c^2=e,b^a=bd,f^a=fg,h^a=h^100,d^b=dg,h^b=h^10,h^c=h^100,h^f=h^100

Conjugacy classes & character table

544 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 20257);