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C₂²×#1568 #6344313

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

Aliases

Subgroups

2274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

(1,2);(3,4);(5,6,7,10,8,9,11,12)(13,14)(15,22)(16,20)(17,26)(18,21)(19,24)(23,27)(25,28);(13,15,17,24,18,25,16,23)(14,19,20,22,21,27,26,28);(6,9)(10,12)(13,16,18,17)(14,20,21,26)(15,23,25,24)(19,22,27,28)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6251509);