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C₂×#51938 #7707946

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

Aliases

Subgroups

8128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615142);