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C₂×#61981 #10578770

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

Aliases

Subgroups

6928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10485966);