Finite Group Databasebeta

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#27300490

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

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

Polycyclic presentation:

2^8,53|a^2=f,b^2=eg,c^2=d,d^2=gh,e^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eg,g^a=gh,i^a=i^52,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, 85966);