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C₂×#18222 #6346493

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

Aliases

Subgroups

3502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6253689);