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C₂×#27677 #6458222

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

Aliases

Subgroups

2902 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6365418);