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C₂×#56114 #8102987

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

Aliases

Subgroups

5384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 34 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 8010183);