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C₂×#34621 #7627778

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

Aliases

Subgroups

6470 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7534974);