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C₂×#23894 #6437590

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

Aliases

Subgroups

5967 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6344786);