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C₂×#51021 #7706651

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

Aliases

Subgroups

6348 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7613847);