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C₂×#44205 #7668162

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

Aliases

Subgroups

5950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7575358);