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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 198 points:
(2,6,7,25,30,3,4,12,14,54)(5,19,20,80,85,9,10,41,43,134)(8,35,36,37,65,16,17,71,73,75)(11,48,49,152,154,22,23,94,95,125)(13,59,60,167,117,27,28,112,114,103)(15,69,40,66,67,32,33,70,31,74)(18,77,78,84,142,38,39,132,115,141)(21,90,91,155,123,45,46,96,138,172)(24,100,101,143,53,51,52,86,140,34)(26,107,108,55,111,56,57,163,104,105)(29,118,119,153,178,62,63,166,170,179)(42,139,102,131,61,82,83,76,161,116)(44,145,146,47,124,87,88,183,68,93)(50,157,158,184,173,97,98,189,151,182)(58,127,128,135,150,110,72,175,92,180)(64,147,169,130,113,121,122,185,171,168)(79,160,164,165,126,99,133,109,181,174)(81,89,120,106,177,136,137,148,162,144)(129,186,159,188,190,176,149,156,187,191)(193,194)(195,196)(197,198);(1,2,5,11,24,53,32,12,26,58,111,161,137,87,41,81,138,181,98,159,91,94,153,188,186,46,92,43,86,144,176,127,17,37,76,100,121,62,27,4,8,18,40,69,125,168,28,61,117,30,65,123,173,83,140,152,163,160,190,150,114,169,189,175,93,151,88,147,119,164,107,39,79,97,48,60,115,82,10,21,47,66,25,55,106,63,120,171,67,71,126,146,141,134,179,78,132,178,85,142,183,174,36,74,130,148,118,162,104,14,31,68,45,19,42,84,112,23,50,99,77,57,109,166,122,145,184,124,128,158,185,167,180,191,133,108,95,143,139,182,172,75,54,103,116,59,113,154,33,70,38,16,6,13,29,64,52,102,73,35,72,129,177,101,80,135,90,149,187,170,49,96,156,157,165,155,136,20,44,89,131,105,110,56,7,15,34,51,22,9,3)(192,193,195,197,198,196,194)
Polycyclic presentation:
2,5,7,191|c^a=c^6,d^a=d^190,d^b=d^39
Conjugacy classes & character table
158 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13370, 12);
Finite Group Databasebeta