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#27300249

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

358 conjugacy classes of subgroups; only the 127 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)(55,62)(56,67)(58,72)(59,74)(60,73)(61,80)(63,83)(64,71)(65,84)(66,86)(68,90)(69,92)(70,91)(75,104)(76,102)(77,101)(78,99)(79,103)(81,97)(82,108)(85,98)(87,89)(88,110)(93,114)(94,113)(95,115)(96,112)(100,105)(106,116)(107,111)(109,117);(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)(54,56,58,68,59,70,76,94,60,69,77,93,79,95,106,109)(55,61,63,66,65,82,75,88,64,81,85,87,78,107,105,96)(57,67,72,90,74,91,102,113,73,92,101,114,103,115,116,117)(62,80,83,86,84,108,104,110,71,97,98,89,99,111,100,112);(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)(56,66,69,87)(57,71,73,62)(58,75)(59,78)(60,64)(61,68,81,93)(63,76)(65,79)(67,89)(70,96,95,88)(72,100,101,104)(74,84,103,99)(77,105)(80,90)(82,109,107,94)(83,102,98,116)(85,106)(86,92)(91,110)(97,114)(108,117)(111,113)(112,115)

Polycyclic presentation:

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

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 85725);