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C₂×#62541 #10579955

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

Aliases

Subgroups

7526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10487151);