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C₂×#12870 #493907

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

Aliases

Subgroups

1138 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

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, 401103);