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C₂×#18557 #6348107

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

Aliases

Subgroups

2928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

(1,2);(3,4,7,9)(5,11,13,18)(6,14,16,10)(8,15,17,12)(19,20,25,30)(21,27,32,33)(22,26,31,34)(23,29,24,28);(3,5,7,13)(4,8,9,17)(6,15,16,12)(10,18,14,11)(19,21,25,32)(20,26,30,34)(22,23,31,24)(27,28,33,29);(19,22)(20,27)(21,23)(24,32)(25,31)(26,28)(29,34)(30,33);(4,9)(8,17)(10,14)(11,18)(19,23,25,24)(20,28,30,29)(21,31,32,22)(26,33,34,27)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6255303);