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Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 111 points:
(1,2)(4,5,7)(6,9,14)(8,12,11)(10,16,24)(13,19,21)(15,22,18)(17,26,37)(20,29,34)(23,32,31)(25,35,28)(27,39,53)(30,42,50)(33,45,47)(36,48,44)(38,51,41)(40,55,71)(43,57,68)(46,60,65)(49,63,62)(52,66,59)(54,69,56)(58,72,85)(61,74,82)(64,77,79)(67,80,76)(70,83,73)(75,86,96)(78,88,93)(81,91,90)(84,94,87)(89,97,104)(92,99,101)(95,102,98)(100,105,109)(103,107,106)(108,110,111);(3,4,6,10,17,27,40,53,68,82,93,101,106,105,88,60,29,9,15,23,33,46,61,75,83,51,24,34,47,62,76,87,86,57,26,38,52,67,81,92,100,102,80,48,22,7,11,18,28,41,56,55,71,85,96,104,109,111,110,99,77,45,19,5,8,13,20,30,43,58,69,37,50,65,79,90,98,97,74,42,16,25,36,49,64,78,89,94,66,35,14,21,31,44,59,73,72,39,54,70,84,95,103,108,107,91,63,32,12)
Conjugacy classes & character table
78 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(654, 2);
Finite Group Databasebeta