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C₂×#20713 #6370901

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

Aliases

Subgroups

4302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278097);