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C₂×#11870 #482035

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

Aliases

Subgroups

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 389231);