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C₂×#59044 #7666855

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

Aliases

Subgroups

9960 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574051);