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C₂×#35774 #7629211

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

Aliases

Subgroups

5864 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7536407);