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C₂×#21750 #6374125

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

Aliases

Subgroups

5566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

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, 6281321);