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C₂×#48564 #7703657

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

Aliases

Subgroups

6956 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)(19,20,24,22)(21,23,26,25);(3,5)(4,7)(6,8)(9,10)(11,12)(13,17)(14,18)(15,16)(19,21)(20,25)(22,23)(24,26);(4,9)(5,6)(12,16)(13,18)(20,22)(21,26);(3,6,8,5)(4,10,9,7)(11,13)(12,14)(15,18)(16,17)(19,22,24,20)(21,23,26,25);(3,7,8,10)(4,5,9,6)(11,14)(12,13)(15,17)(16,18)(19,23)(20,21)(22,26)(24,25)

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, 7610853);