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C₂×#53908 #8102293

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

Aliases

Subgroups

7780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8009489);