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C₂×#15694 #609333

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

Aliases

Subgroups

5266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 516529);