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C₂×#11389 #358799

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

Aliases

Subgroups

2670 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 265995);