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C₂×#13283 #495371

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

Aliases

Subgroups

1022 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 402567);