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C₂×#2770 #52209

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

Aliases

Subgroups

1035 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 45197);