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C₂×#11132 #357820

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

Aliases

Subgroups

2690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265016);