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C₂×#13264 #495324

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

Aliases

Subgroups

1006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 30 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402520);