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C₂×#13066 #494643

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

Aliases

Subgroups

1358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,11,16,13,17,12,28)(9,18,20,35,21,34,27,36)(10,22,24,30,26,38,25,15)(14,29,31,19,33,37,32,23);(7,9,10,23,12,20,25,29,13,21,26,19,11,27,24,37)(8,14,30,18,16,32,38,36,17,33,15,34,28,31,22,35);(4,6)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401839);