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C₂×#33520 #7622810

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

Aliases

Subgroups

4174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530006);