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D₄₇×#3556 #27124111

• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

Splittings

Subgroups

6338 conjugacy classes of subgroups.

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)(64,68,69,67)(65,71,72,77)(66,74,75,76)(70,79,73,78);(49,55)(53,62)(54,58)(61,63)(64,67,69,68)(65,71,72,77)(66,74,75,76)(70,78,73,79);(48,51,52,60)(49,54,55,58)(50,56,57,59)(53,61,62,63);(48,50,52,57)(49,53,55,62)(51,59,60,56)(54,63,58,61)(64,66,69,75)(65,70,72,73)(67,76,68,74)(71,79,77,78);(48,49)(50,53)(51,58)(52,55)(54,60)(56,63)(57,62)(59,61)(64,65,69,72)(66,73,75,70)(67,71,68,77)(74,79,76,78);(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, 1077401);