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C₂×#9489 #201532

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

Aliases

Subgroups

1706 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 108728);