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C₂×#30498 #7500917

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

Aliases

Subgroups

3140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7408113);