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C₂×#17744 #6344034

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

Aliases

Subgroups

4288 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6251230);