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C₂×#54819 #8102116

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

Aliases

Subgroups

5924 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)(21,24)(22,26)(23,25);(3,4,7,8)(5,6,9,10)(11,13)(12,16)(14,17)(15,18)(19,21,23,26)(20,24,25,22);(4,8)(5,9)(11,14,15,16)(12,13,17,18)(19,21)(20,22)(23,26)(24,25);(3,5)(4,6)(7,9)(8,10)(11,14)(12,13)(15,16)(17,18)(19,22)(20,21)(23,24)(25,26);(3,6)(4,5)(7,10)(8,9)(11,12)(13,14)(15,17)(16,18)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8009312);