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C₂×#48270 #7703330

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

Aliases

Subgroups

5656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610526);