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#72234407

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Subgroups

1026 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 288 points:

(1,2,3,7,4,8,11,17,5,9,12,18,14,20,23,27,6,10,13,19,15,21,24,28,16,22,25,29,26,30,31,32)(33,34,36,46,39,49,67,106,41,50,69,108,84,118,173,232,43,51,71,109,88,122,171,237,93,124,68,179,85,119,174,233,44,52,72,110,89,123,178,231,92,125,180,107,83,200,172,236,42,94,70,181,82,199,177,279,40,90,91,203,38,48,66,105)(35,53,54,126,57,129,135,224,60,130,137,251,154,222,205,225,62,131,139,234,86,45,95,96,58,98,158,210,152,100,206,211,63,132,140,252,157,101,207,212,59,120,64,162,56,128,134,250,61,161,138,265,151,102,208,213,159,221,136,264,153,99,175,103)(37,73,74,183,76,185,189,282,78,47,111,112,190,114,238,241,80,115,65,164,155,245,166,276,197,116,168,104,75,184,188,227,81,186,169,228,87,113,202,240,160,117,167,229,191,121,165,247,79,198,170,242,194,243,176,226,77,195,196,230,192,248,277,235)(55,141,142,266,144,217,204,239,147,255,259,288,143,256,267,285,149,246,133,257,193,281,258,223,145,271,260,287,269,97,214,215,150,216,261,274,156,218,273,286,146,127,187,253,270,219,278,209,148,244,262,283,201,182,263,280,272,254,163,249,268,220,275,284);(33,35,37,55,40,58,77,145,42,61,79,148,92,60,160,147,44,63,81,150,93,159,197,272,43,62,80,149,41,59,78,146)(34,45,47,97,50,99,115,217,51,101,116,219,124,222,186,281,52,102,117,220,125,100,198,218,94,129,195,256,90,128,73,182)(36,64,65,163,68,140,167,262,70,158,74,187,69,139,168,261,72,137,170,260,91,54,111,133,71,136,169,259,180,138,196,142)(38,56,75,143,82,57,155,156,83,152,190,268,89,151,76,193,85,154,192,270,88,157,194,144,84,153,191,269,39,86,87,201)(46,103,104,223,107,224,183,215,109,225,229,286,203,96,164,209,110,211,230,280,108,212,228,284,181,250,112,239,179,213,242,285)(48,53,113,127,49,120,121,246,118,131,243,254,122,221,248,216,119,132,185,255,123,130,114,244,200,161,245,271,199,98,184,141)(66,95,165,204,171,205,189,275,172,135,188,263,67,175,176,278,174,208,238,273,177,134,202,214,173,207,277,258,178,206,166,267)(105,162,226,274,231,265,227,253,232,264,282,283,279,126,247,249,233,251,276,266,106,234,235,288,236,210,240,257,237,252,241,287)

Polycyclic presentation:

2^13|a^2=c,b^2=d,c^2=f,d^2=g,e^2=hkm,f^2=i,g^2=j,h^2=k,i^2=l,j^2=m,k^2=m,l^2=m,b^a=be,c^b=ch,d^a=dhkm,d^c=dkm,f^b=fk,f^d=fm,g^a=gkm,g^c=gm,i^b=im,j^a=jm

Conjugacy classes & character table

752 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m");;
gap> coll := SingleCollector(F, [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]);;
gap> SetPower(coll, 1, F.3);;
gap> SetPower(coll, 2, F.4);;
gap> SetPower(coll, 3, F.6);;
gap> SetPower(coll, 4, F.7);;
gap> SetPower(coll, 5, F.8*F.11*F.13);;
gap> SetPower(coll, 6, F.9);;
gap> SetPower(coll, 7, F.10);;
gap> SetPower(coll, 8, F.11);;
gap> SetPower(coll, 9, F.12);;
gap> SetPower(coll, 10, F.13);;
gap> SetPower(coll, 11, F.13);;
gap> SetPower(coll, 12, F.13);;
gap> SetConjugate(coll, 2, 1, F.2*F.5);;
gap> SetConjugate(coll, 3, 2, F.3*F.8);;
gap> SetConjugate(coll, 4, 1, F.4*F.8*F.11*F.13);;
gap> SetConjugate(coll, 4, 3, F.4*F.11*F.13);;
gap> SetConjugate(coll, 6, 2, F.6*F.11);;
gap> SetConjugate(coll, 6, 4, F.6*F.13);;
gap> SetConjugate(coll, 7, 1, F.7*F.11*F.13);;
gap> SetConjugate(coll, 7, 3, F.7*F.13);;
gap> SetConjugate(coll, 9, 2, F.9*F.13);;
gap> SetConjugate(coll, 10, 1, F.10*F.13);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);