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C₂×#36488 #7630173

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

Aliases

Subgroups

6786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7537369);