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C₂×#9889 #206957

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

Aliases

Subgroups

1662 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 114153);