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C₂×#61594 #10577197

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

Aliases

Subgroups

8062 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10484393);