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C₂×#11485 #480126

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

Aliases

Subgroups

1010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 387322);