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C₂×#59940 #7666147

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

Aliases

Subgroups

8654 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7573343);