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C₂×#29853 #6435530

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

Aliases

Subgroups

2500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6342726);