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C₂×#11872 #482037

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

Aliases

Subgroups

1008 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 389233);