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C₂×#17367 #6342562

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

Aliases

Subgroups

4770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6249758);