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C₂×#24297 #6442697

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

Aliases

Subgroups

4602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6349893);