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C₂×#33656 #7623058

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

Aliases

Subgroups

1616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530254);