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C₂×#11172 #357888

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

Aliases

Subgroups

3658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265084);