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C₂×#12589 #492910

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

Aliases

Subgroups

2362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400106);