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C₂×#9609 #203712

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

Aliases

Subgroups

696 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 110908);