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C₂×#12948 #494318

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

Aliases

Subgroups

1036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 401514);