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C₂×#30497 #7500916

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

Aliases

Subgroups

3092 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7408112);