Finite Group Databasebeta

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D₄₇×#3550 #27124082

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

Aliases

Splittings

Subgroups

7074 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)(56,60,61,59)(57,63,64,69)(58,66,67,68)(62,71,65,70);(49,53)(52,54)(56,59,61,60)(57,63,64,69)(58,66,67,68)(62,70,65,71);(48,50,51,55)(49,52,53,54);(50,55)(52,54)(56,58,61,67)(57,62,64,65)(59,68,60,66)(63,71,69,70);(48,49)(50,54)(51,53)(52,55)(56,57,61,64)(58,65,67,62)(59,63,60,69)(66,71,68,70);(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)

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, 1077372);