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C₂×#12826 #493792

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

Aliases

Subgroups

1120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400988);