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C₂×#62831 #10586179

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

Aliases

Subgroups

31992 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493375);