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C₂×#44813 #7669205

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

Aliases

Subgroups

6782 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7576401);