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C₂×#20495 #6370024

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

Aliases

Subgroups

3422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277220);