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C₂×#59210 #7666697

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

Aliases

Subgroups

6268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573893);