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C₂×#48415 #7703993

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

Aliases

Subgroups

8140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7611189);