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C₂×#12577 #492890

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

Aliases

Subgroups

2402 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4)(5,13)(6,17,18,10)(7,11)(8,12)(9,15,21,27)(14,25)(16,26)(19,30,31,23)(20,24)(22,29,32,34)(28,33);(3,5,7,16,8,14,20,28)(4,9,11,22,12,21,24,32)(6,15,19,29,18,27,31,34)(10,13,23,26,17,25,30,33);(5,14)(9,21)(13,25)(15,27)(16,28)(22,32)(26,33)(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, 400086);