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C₂×#11234 #358046

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

Aliases

Subgroups

1814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265242);