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C₂×#53994 #8100413

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

Aliases

Subgroups

6556 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8007609);