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C₂×#17917 #6344624

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

Aliases

Subgroups

2006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6251820);