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C₂×#62870 #10586202

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

Aliases

Subgroups

32646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493398);