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C₂×#61673 #10577278

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

Aliases

Subgroups

8000 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

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

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, 10484474);