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C₂×#36794 #7634004

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

Aliases

Subgroups

8300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7541200);