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C₂×#49945 #7705362

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

Aliases

Subgroups

7154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,9)(6,7)(8,10)(19,20,23,25)(21,22,26,24);(3,5)(4,8)(6,9)(7,10)(12,15)(13,17)(19,21)(20,24)(22,25)(23,26);(5,10)(8,9)(11,12,14,15)(13,16,17,18)(19,21,23,26)(20,24,25,22);(3,5)(4,9)(6,8)(7,10)(11,12)(13,16)(14,15)(17,18)(19,21)(20,22)(23,26)(24,25);(3,6,7,4)(5,8,10,9)(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, 7612558);