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C₂×#14450 #520789

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

Aliases

Subgroups

5418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 427985);