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C₂×#12808 #493736

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

Aliases

Subgroups

1124 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400932);