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C₂×#18559 #6348109

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

Aliases

Subgroups

2998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6255305);