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C₂×#36211 #7629853

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

Aliases

Subgroups

7274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537049);