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C₂×#3554 #62746

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

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, 55734);