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C₂×#33595 #7622950

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

Aliases

Subgroups

2108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7530146);