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C₂×#62948 #10586292

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

Aliases

Subgroups

32176 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 34 points:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493488);