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C₂×#49758 #7705356

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

Aliases

Subgroups

6364 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)(11,12,16,18)(13,17,14,15);(3,5)(4,8)(6,9)(7,10)(11,13)(12,17)(14,16)(15,18)(20,23)(21,25);(5,10)(8,9)(12,18)(13,14)(19,20,22,23)(21,24,25,26);(3,5)(4,9)(6,8)(7,10)(11,14,16,13)(12,15,18,17)(19,20)(21,24)(22,23)(25,26);(3,6,7,4)(5,8,10,9)(11,15)(12,13)(14,18)(16,17)(19,21)(20,24)(22,25)(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, 7612552);