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C₂×#50015 #7705317

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

Aliases

Subgroups

8268 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612513);