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C₂×#12709 #493400

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

Aliases

Subgroups

3424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

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

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, 400596);