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C₂×#59962 #7666970

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

Aliases

Subgroups

6250 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7574166);