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C₂×#60219 #10574249

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481445);