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C₂×#47565 #7701512

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

Aliases

Subgroups

6598 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,8)(6,10)(11,12)(13,15)(14,16)(17,18);(3,4,7,8)(5,10,9,6)(11,12)(13,17)(14,16)(15,18)(19,20,23,25)(21,22,26,24);(4,8)(5,9)(11,12,14,16)(13,15,18,17)(19,21,23,26)(20,24,25,22);(3,5,7,9)(4,6,8,10)(11,12)(13,15)(14,16)(17,18)(19,21)(20,22)(23,26)(24,25);(3,6)(4,9)(5,8)(7,10)(11,13)(12,15)(14,18)(16,17)(19,22)(20,21)(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, 7608708);