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C₂×#17403 #6342637

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

Aliases

Subgroups

4304 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6249833);