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C₂×#7975 #181213

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

Aliases

Subgroups

1678 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 88409);