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C₂×#49837 #7705026

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

Aliases

Subgroups

6278 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612222);