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C₂×#50104 #7705659

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

Aliases

Subgroups

6556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612855);