Finite Group Databasebeta

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#34115204

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 189 points:

(1,2,5,10,19,32,49,70,95,124,118,91,116,140,134,101,72,47,67,90,115,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,148,151,144,120,142,137,105,76,51,30,46,65,86,111,131,102,77,56,39,26,15,24,37,54,75,100,129,149,155,157,153,146,139,109,80,55,34,17,29,44,61,82,107,135,106,81,60,43,28,41,58,79,104,133,122,147,154,156,150,141,113,84,59,38,21,8,16,27,40,57,78,103,132,110,85,64,45,62,83,108,136,126,93,121,145,152,143,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,114,89,66,87,112,138,130,97,68,92,119,123,94,69,48,31,18,9,4)(158,160,162,173,178,187,176,185,164,172,175,186,163,174,161,171)(159,165,167,181,179,188,166,170,169,180,183,189,168,182,177,184);(2,3,4,6)(5,8,9,15)(7,12,13,11)(10,17,18,28)(14,21,22,24)(16,25,26,20)(19,30,31,45)(23,34,35,41)(27,38,39,37)(29,42,43,33)(32,47,48,66)(36,51,52,62)(40,55,56,58)(44,59,60,54)(46,63,64,50)(49,68,69,91)(53,72,73,87)(57,76,77,83)(61,80,81,79)(65,84,85,75)(67,88,89,71)(70,93,94,120)(74,97,98,116)(78,101,102,112)(82,105,106,108)(86,109,110,104)(90,113,114,100)(92,117,118,96)(95,122,123,146)(99,126,127,142)(103,130,131,140)(107,134,135,138)(111,137,132,136)(115,139,128,133)(119,141,124,129)(121,143,144,125)(145,150,151,149)(147,152,153,148)(154,156,157,155)(158,159)(160,170,172,184)(161,167)(162,177)(163,179)(164,169)(165,171,180,185)(166,175)(168,178)(173,188,186,182)(174,189,187,181)(176,183)

Polycyclic presentation:

2^7,157|a^2=d,b^2=e,c^2=f,e^2=fg,f^2=g,b^a=bc,c^a=cf,e^a=ef,f^a=fg,h^a=h^129,d^b=dg,h^d=h^156

Conjugacy classes & character table

1280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20096, 19578);