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C₂×#27601 #6457022

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

Aliases

Subgroups

3646 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)(11,12,14,16)(13,15,17,18)(19,20,22,25)(21,23,26,24);(4,7)(8,10)(11,13)(12,15)(14,17)(16,18);(3,5,6,9)(4,8,7,10)(13,17)(15,18)(20,23)(21,26)(24,25);(4,7)(8,10)

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, 6364218);