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C₂×#8556 #188075

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

Aliases

Subgroups

2802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,7,12,8,11,6,10)(5,13,14,18,15,9,16,17)(19,20)(21,24)(22,29,30,25)(23,26)(27,33,34,31)(28,32);(3,5)(4,9)(6,14)(7,16)(8,15)(10,17)(11,13)(12,18)(19,21,23,28)(20,24,26,32)(22,27,30,34)(25,31,29,33);(3,6,8,7)(4,10,11,12)(5,14,15,16)(9,17,13,18)(19,22,23,30)(20,25,26,29)(21,27,28,34)(24,31,32,33)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 95271);