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C₂×#61417 #10576707

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

Aliases

Subgroups

7158 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10483903);