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C₂×#43772 #7667865

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

Aliases

Subgroups

6284 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)(11,12,16,14)(13,17,15,18)(19,20)(21,22)(23,26)(24,25);(3,4,6,7)(5,9,10,8)(12,14)(13,15)(20,25)(22,26);(4,7)(8,9)(11,13,16,15)(12,17,14,18)(19,21,24,23)(20,22,25,26);(3,4)(5,8)(6,7)(9,10)(11,14,16,12)(13,17,15,18)(19,22,24,26)(20,21,25,23);(3,5,6,10)(4,8,7,9)(11,15,16,13)(12,17,14,18)(19,23,24,21)(20,26,25,22)

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, 7575061);