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C₂×#11094 #357774

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

Aliases

Subgroups

2698 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)(5,10,17,25,16,26,15,31)(6,18,21,11,20,28,23,27)(14,29,30,24,19,33,32,34);(3,5)(4,10)(6,19,20,14)(7,15)(8,17)(9,16)(11,24,27,34)(12,25)(13,26)(18,29,28,33)(21,32,23,30)(22,31);(3,6)(4,11)(5,14)(7,23)(8,21)(9,20)(10,24)(12,28)(13,27)(15,32)(16,19)(17,30)(18,22)(25,33)(26,34)(29,31)

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, 264970);