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C₂×#33966 #7623955

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

Aliases

Subgroups

1580 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531151);