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C₂×#35914 #7629219

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

Aliases

Subgroups

7578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7536415);