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C₂×#61095 #10576088

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

Aliases

Subgroups

10780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483284);