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C₂×#25773 #6443347

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

Aliases

Subgroups

6048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6350543);