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Aliases
Splittings
Subgroups
At least 6438 conjugacy classes of subgroups; only the 3217 normal subgroups are shown.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 6 generators on 79 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)(49,55)(53,56)(54,61)(60,62)(64,67,68,74)(65,71,70,77)(66,73,72,78)(69,76,75,79);(50,58)(53,56)(57,63)(60,62)(65,70)(69,75)(71,77)(76,79);(48,51,52,59)(49,54,55,61)(50,57,58,63)(53,60,56,62)(65,70)(66,72)(71,77)(73,78);(48,50)(49,53)(51,57)(52,58)(54,60)(55,56)(59,63)(61,62)(64,66)(65,69)(67,73)(68,72)(70,75)(71,76)(74,78)(77,79);(48,49)(50,56)(51,54)(52,55)(53,58)(57,62)(59,61)(60,63)(64,65)(66,69)(67,71)(68,70)(72,75)(73,76)(74,77)(78,79);(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)
Conjugacy classes & character table
950 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12032, 1077088);
Finite Group Databasebeta