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C₂×#14347 #515261

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

Aliases

Subgroups

6106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 422457);