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C₂×#11115 #357781

• 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)(6,18,21,11)(7,22)(8,12)(9,13)(10,16)(15,31,33,28)(17,27)(19,25,32,34)(20,29,24,30)(23,26);(3,5,7,16,9,17,8,23)(4,10,12,14,13,26,22,27)(6,19,20,15,21,32,24,33)(11,28,29,34,18,31,30,25);(3,6)(4,11)(5,15)(7,20)(8,24)(9,21)(10,25)(12,29)(13,18)(14,28)(16,32)(17,33)(19,23)(22,30)(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, 264977);