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C₂×#27539 #6440965

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

Aliases

Subgroups

3346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6348161);