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C₂×#57217 #8101006

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

Aliases

Subgroups

6678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8008202);