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C₂×#24288 #6442594

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

Aliases

Subgroups

4450 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6349790);