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C₂×#56283 #8102864

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

Aliases

Subgroups

5962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8010060);