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C₂×#17572 #6343343

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

Aliases

Subgroups

5174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250539);