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C₂×#62825 #10586173

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

Aliases

Subgroups

31998 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)(20,25)(21,29)(22,32)(28,33);(5,11)(9,14)(12,17)(16,18)(19,20,24,25)(21,30,29,26)(22,27,32,34)(23,33,31,28);(3,4,7,8)(5,9,11,14)(6,10,13,15)(12,16,17,18)(19,21,24,29)(20,26,25,30)(22,31,32,23)(27,33,34,28);(19,22)(20,27)(21,31)(23,29)(24,32)(25,34)(26,33)(28,30);(3,5)(4,9)(6,12)(7,11)(8,14)(10,16)(13,17)(15,18)(19,23,24,31)(20,28,25,33)(21,22,29,32)(26,27,30,34);(3,6)(4,10)(5,12)(7,13)(8,15)(9,16)(11,17)(14,18)(19,22)(20,27)(21,31)(23,29)(24,32)(25,34)(26,33)(28,30)

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, 10493369);