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C₂×#46862 #7700610

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

Aliases

Subgroups

6818 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7607806);