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#27301284

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

456 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

Full subgroup data →

Presentation

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

Polycyclic presentation:

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

Conjugacy classes & character table

872 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 86760);