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C₂×#12743 #493539

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

Aliases

Subgroups

3276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400735);