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Aliases
Splittings
Subgroups
72 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 3 generators on 162 points:
(1,2,3,4,5,6,7)(9,10)(12,13)(15,16,17,19)(18,21,22,28)(20,25,26,24)(23,30,31,41)(27,34,35,37)(29,38,39,33)(32,43,44,58)(36,47,48,54)(40,51,52,50)(42,55,56,46)(45,60,61,79)(49,64,65,75)(53,68,69,71)(57,72,73,67)(59,76,77,63)(62,81,82,104)(66,85,86,100)(70,89,90,96)(74,93,94,92)(78,97,98,88)(80,101,102,84)(83,106,107,133)(87,110,111,129)(91,114,115,125)(95,118,119,121)(99,122,123,117)(103,126,127,113)(105,130,131,109)(108,135,136,158)(112,139,140,156)(116,143,144,154)(120,147,148,152)(124,151,149,150)(128,153,145,146)(132,155,141,142)(134,157,137,138)(159,161,162,160);(11,12,13)(14,15,18,23,32,45,62,83,108,137,133,156,153,122,93,68,47,30,42,57,74,95,120,149,123,98,77,58,75,96,121,150,143,110,81,105,132,140,111,86,65,48,35,26,19,24,33,46,63,84,109,138,160,162,158,155,126,97,72,51,34,21,29,40,53,70,91,116,145,127,102,79,100,125,152,147,114,85,60,80,103,128,144,115,90,69,52,39,28,37,50,67,88,113,142,135,159,161,157,130,101,76,55,38,25,16,20,27,36,49,66,87,112,141,131,104,129,154,151,118,89,64,43,59,78,99,124,148,119,94,73,56,41,54,71,92,117,146,139,106,134,136,107,82,61,44,31,22,17);(8,9,10)
Conjugacy classes & character table
2415 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37548, 108);
Finite Group Databasebeta