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D₄₇×#3535 #27123471

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

7302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 71 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)(57,63)(61,64)(62,71)(69,70);(49,53)(52,55)(56,59,60,68)(57,62,63,71)(58,65,66,67)(61,69,64,70);(49,53)(50,54);(48,50)(49,52)(51,54)(53,55)(56,58,60,66)(57,61,63,64)(59,67,68,65)(62,70,71,69);(48,49)(50,52)(51,53)(54,55)(56,57)(58,64)(59,62)(60,63)(61,66)(65,70)(67,69)(68,71);(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, 1076761);