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C₂×#40698 #7639000

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

Aliases

Subgroups

7332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546196);