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C₂×#38166 #7635435

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

Aliases

Subgroups

6202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7542631);