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C₂×#48023 #7703181

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

Aliases

Subgroups

5898 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(11,12,15,17)(13,14,18,16)(19,20,23,21)(22,25,26,24);(3,4)(5,9)(6,10)(7,8)(11,13,15,18)(12,16,17,14)(19,21,23,20)(22,25,26,24);(4,8)(5,10)(11,14)(12,13)(15,16)(17,18)(19,22,23,26)(20,24,21,25);(3,5)(4,6)(7,10)(8,9)(11,13)(12,14)(15,18)(16,17);(3,6)(4,5)(7,9)(8,10)(11,14)(12,13)(15,16)(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, 7610377);