Finite Group Databasebeta

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#27304627

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

180 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 125 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,57,60)(55,59,58,61)(64,74)(69,84)(75,94)(76,95)(77,96)(85,104)(86,105)(87,106)(97,114)(98,115)(99,116)(107,119)(108,120)(109,121)(117,124)(122,125);(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)(55,58)(59,61)(62,64)(63,69)(65,75)(66,76)(67,77)(68,74)(70,85)(71,86)(72,87)(73,84)(78,97)(79,98)(80,94)(81,99)(82,95)(83,96)(88,107)(89,108)(90,104)(91,109)(92,105)(93,106)(100,117)(101,114)(102,115)(103,116)(110,122)(111,119)(112,120)(113,121)(118,124)(123,125);(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)(56,59)(57,58)(60,61)(62,63,65,70,66,71,78,88,67,72,79,89,81,91,100,110,68,73,80,90,82,92,101,111,83,93,102,112,103,113,118,123)(64,69,75,85,76,86,97,107,77,87,98,108,99,109,117,122,74,84,94,104,95,105,114,119,96,106,115,120,116,121,124,125)

Polycyclic presentation:

2^8,53|a^2=e,c^2=d,e^2=f,f^2=g,g^2=h,b^a=bd,i^a=i^52,c^b=ch,i^b=i^52

Conjugacy classes & character table

2192 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 90103);