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C₂×#25712 #6450127

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

Aliases

Subgroups

3408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6357323);