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C₂×#28243 #6465503

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

Aliases

Subgroups

2726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6372699);