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C₂×#23999 #6451731

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

Aliases

Subgroups

3840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6358927);