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C₂×#54920 #8098888

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

Aliases

Subgroups

6910 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 8006084);