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C₂×#22405 #6379007

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

Aliases

Subgroups

5778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6286203);