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C₂×#41430 #7639764

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

Aliases

Subgroups

5822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546960);