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C₂×#48060 #7703516

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

Aliases

Subgroups

6202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4,7,9)(5,10,6,8)(19,20,23,25)(21,22,26,24);(3,5,7,6)(4,8,9,10)(11,12)(13,17)(14,18)(15,16)(19,21,23,26)(20,24,25,22);(5,6)(8,10)(12,16)(13,18)(19,22)(20,21)(23,24)(25,26);(3,6,7,5)(4,8,9,10)(11,13)(12,14)(15,18)(16,17)(19,21)(20,22)(23,26)(24,25);(3,4)(5,10)(6,8)(7,9)(11,14)(12,13)(15,17)(16,18)(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, 7610712);