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C₂×#11559 #480502

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

Aliases

Subgroups

1568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 387698);