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C₂×#32705 #7513956

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

Aliases

Subgroups

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7421152);