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C₂×#47905 #7703481

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

Aliases

Subgroups

6202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610677);