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C₂×#25587 #6449103

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

Aliases

Subgroups

4322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6356299);