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C₂×#20228 #6359582

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

Aliases

Subgroups

1677 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6266778);