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C₂×#48009 #7703671

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

Aliases

Subgroups

6764 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610867);