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C₂×#25635 #6449200

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

Aliases

Subgroups

3886 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 6356396);