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C₂×#11868 #482029

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

Aliases

Subgroups

1080 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 389225);