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Aliases
Splittings
Subgroups
7398 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 6 generators on 73 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(59,65)(63,66)(64,69)(72,73);(50,52,53,56)(51,55,54,57)(59,65)(60,68)(64,69)(67,70);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(50,51)(52,55)(53,54)(56,57)(58,61,62,71)(59,64,65,69)(60,67,68,70)(63,72,66,73);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(51,54)(55,57)(58,60)(59,63)(61,70)(62,68)(64,73)(65,66)(67,71)(69,72);(51,54)(52,56)(58,59)(60,66)(61,69)(62,65)(63,68)(64,71)(67,72)(70,73);(48,49)
Conjugacy classes & character table
1088 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1076993);
Finite Group Databasebeta