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C₂×#44214 #7668397

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

Aliases

Subgroups

7192 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)(13,16)(14,15)(17,18)(19,20,23,25)(21,26,24,22);(4,7)(8,10)(12,14)(13,17)(19,21,23,24)(20,22,25,26);(11,13,15,17)(12,16,14,18)(19,22,23,26)(20,24,25,21);(3,4)(5,8)(6,7)(9,10)(11,13)(12,16)(14,18)(15,17)(19,22)(20,21)(23,26)(24,25);(3,5,6,9)(4,8,7,10)(11,14,15,12)(13,18,17,16)(19,21)(20,22)(23,24)(25,26)

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, 7575593);