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C₂×#10831 #353556

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

Aliases

Subgroups

1774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260752);