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C₂×#24001 #6451732

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

Aliases

Subgroups

3770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6358928);