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Aliases
Subgroups
604 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3)(4,5)(6,15)(7,19)(8,23)(9,14)(10,17)(11,18)(12,21)(13,24)(16,30)(20,25)(22,33)(26,32)(27,34)(28,31)(29,35);(4,6)(5,10,14,26)(7,16)(8,17)(9,18)(11,13,15,23)(12,25,29,30)(19,28,33,27)(20,22)(21,31)(24,32)(34,35);(4,6)(5,11,14,15)(7,20)(8,17)(9,18)(10,23,26,13)(12,28,29,27)(16,22)(19,30,33,25)(21,34)(24,32)(31,35);(4,7,8,21,9,22,24,35)(5,12,13,19,14,29,23,33)(6,16,17,31,18,20,32,34)(10,25,15,28,26,30,11,27)
Conjugacy classes & character table
120 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 22259);
Finite Group Databasebeta