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C₂×#11886 #482071

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

Aliases

Subgroups

1310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 389267);