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C₂×#49749 #7705090

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

Aliases

Subgroups

7080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612286);