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C₂×#3547 #62750

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

Aliases

Subgroups

3591 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 55738);