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C₂×#56299 #8099031

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

Aliases

Subgroups

7310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8006227);