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C₂×#22279 #6376427

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

Aliases

Subgroups

2938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6283623);