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C₂×#17753 #6344045

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

Aliases

Subgroups

3356 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6251241);