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C₂×#11100 #357680

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

Aliases

Subgroups

3382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 264876);