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C₂×#61077 #10576084

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

Aliases

Subgroups

10682 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)(9,18)(10,17)(11,15)(12,14)(13,16)(19,22)(20,21);(7,9)(8,11)(10,15)(12,21)(13,19)(14,18)(16,20)(17,22);(4,6)(7,10,13,12)(8,14,16,17)(9,15,19,21)(11,18,20,22);(7,11,13,20)(8,15,16,21)(9,14,19,17)(10,18,12,22);(8,16)(9,19)(14,17)(15,21)

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, 10483280);