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C₂×#19751 #6357771

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

Aliases

Subgroups

1968 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6264967);