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C₂²×#97×C₃₇ #17991688

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 53 points:

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

Conjugacy classes & character table

2960 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1602);