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C₂×#25170 #6438638

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

Aliases

Subgroups

3616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345834);