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C₂×#59570 #7666161

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

Aliases

Subgroups

6664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7573357);