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C₂×#19748 #6357767

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

Aliases

Subgroups

2324 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6264963);