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C₂×#24474 #6437947

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

Aliases

Subgroups

4489 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6345143);