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C₂×#10690 #244493

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

Aliases

Subgroups

1014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 151689);