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C₂×#37215 #7634576

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

Aliases

Subgroups

5532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7541772);