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C₂×#7474 #151773

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

Aliases

Subgroups

398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 38 points:

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

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, 58969);