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C₂×#57222 #8100595

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

Aliases

Subgroups

6716 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)(11,12,15,17)(13,14,18,16)(19,20,24,25)(21,23,22,26);(4,7)(8,9)(11,13,15,18)(12,16,17,14)(20,25)(21,22);(12,17)(14,16)(19,21,24,22)(20,26,25,23);(3,4)(5,8)(6,7)(9,10)(11,14,15,16)(12,13,17,18)(19,22,24,21)(20,23,25,26);(3,5)(4,8)(6,10)(7,9)(11,13)(12,16)(14,17)(15,18)(19,23)(20,21)(22,25)(24,26)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8007791);