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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 168 points:
(1,2,3,4,5)(6,7)(8,10,11,9)(13,14,15,17)(16,19,20,26)(18,23,24,22)(21,28,29,39)(25,32,33,35)(27,36,37,31)(30,41,42,56)(34,45,46,52)(38,49,50,48)(40,53,54,44)(43,58,59,77)(47,62,63,73)(51,66,67,69)(55,70,71,65)(57,74,75,61)(60,79,80,102)(64,83,84,98)(68,87,88,94)(72,91,92,90)(76,95,96,86)(78,99,100,82)(81,104,105,131)(85,108,109,127)(89,112,113,123)(93,116,117,119)(97,120,121,115)(101,124,125,111)(103,128,129,107)(106,133,134,146)(110,137,138,157)(114,135,141,155)(118,144,145,151)(122,148,149,147)(126,152,153,143)(130,156,154,140)(132,158,150,136)(139,159,160,164)(142,161,162,165)(163,166,167,168);(6,8,11)(7,10,9)(12,13,16,21,30,43,60,81,106,135,108,79,103,130,153,125,100,77,98,123,151,158,128,99,74,53,36,23,14,18,25,34,47,64,85,110,139,161,137,104,132,149,121,96,75,56,73,94,119,147,156,124,95,70,49,32,19,27,38,51,68,89,114,142,163,166,159,133,145,117,92,71,54,39,52,69,90,115,143,152,120,91,66,45,28,40,55,72,93,118,146,164,168,167,162,141,113,88,67,50,37,26,35,48,65,86,111,140,148,116,87,62,41,57,76,97,122,150,131,157,165,160,138,109,84,63,46,33,24,17,22,31,44,61,82,107,136,144,112,83,58,78,101,126,154,129,102,127,155,134,105,80,59,42,29,20,15)
Conjugacy classes & character table
1785 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28260, 102);
Finite Group Databasebeta