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C₂×#10905 #353939

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

Aliases

Subgroups

1926 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261135);