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C₂×#29270 #6463581

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

Aliases

Subgroups

1722 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6370777);