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C₂×#11103 #357685

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

Aliases

Subgroups

2618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 264881);