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C₂×#42872 #7641410

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

Aliases

Subgroups

6302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548606);