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C₂×#33072 #6629542

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

2546 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

(1,2);(3,4,6,7)(5,8,9,10)(11,12)(13,15)(14,16)(17,18)(19,20,21,23)(22,24,26,25);(4,7)(8,10)(11,13,14,17)(12,15,16,18)(20,23)(24,25);(3,5,6,9)(4,8,7,10)(12,16)(15,18)(20,23)(24,25);(20,24)(22,26)(23,25)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6536738);