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C₂×#31396 #7504595

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

Aliases

Subgroups

2778 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7411791);