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C₂×#27312 #6440878

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

Aliases

Subgroups

2184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6348074);