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C₂×#21477 #6372719

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

Aliases

Subgroups

4452 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6279915);