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C₂×#48839 #7704184

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

Aliases

Subgroups

6094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7611380);