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C₂×#40721 #7638681

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

Aliases

Subgroups

7208 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7545877);