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C₂×#36464 #7630146

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

Aliases

Subgroups

6614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537342);