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C₂×#11360 #358610

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

Aliases

Subgroups

1614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 265806);