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C₂×#47849 #7703176

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

Aliases

Subgroups

8324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

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, 7610372);