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C₂×#23784 #6432533

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

Aliases

Subgroups

2130 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)(11,12,14,16)(13,17,18,15)(20,23)(24,26);(4,7)(8,10)(20,24)(22,25)(23,26);(11,13,14,18)(12,15,16,17)(19,20,21,23)(22,26,25,24);(3,5,6,9)(4,8,7,10)(20,23)(24,26)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339729);