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C₂×#12717 #493416

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

Aliases

Subgroups

3284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400612);