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D₄₇×#2952 #27080435

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

2806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 67 points:

(5,9,11,7)(6,14,15,17)(8,16,10,18)(12,13,20,19)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(1,3,4,2)(5,8,11,10)(6,13,15,19)(7,16,9,18)(12,17,20,14);(5,7,11,9)(6,12,15,20)(8,16,10,18)(13,17,19,14);(1,2,4,3)(5,6,11,15)(7,14,9,17)(8,13,10,19)(12,18,20,16);(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)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)

Conjugacy classes & character table

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033725);