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C₂×#12988 #494431

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

Aliases

Subgroups

1298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401627);