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C₂×#36198 #7629837

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

Aliases

Subgroups

7048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7537033);