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C₂×#20710 #6370896

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

Aliases

Subgroups

4382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278092);