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C₂×#2577 #34846

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

Aliases

Subgroups

1091 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27834);