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C₂×#12757 #493566

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

Aliases

Subgroups

2367 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400762);