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C₂×#28715 #6466490

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

Aliases

Subgroups

2294 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)(10,12)(11,14)(15,16)(17,20)(18,21)(19,22)(23,30)(24,28)(25,27)(26,29);(7,9,11,10)(8,12,14,13)(15,17,19,25,18,24,26,23)(16,20,22,27,21,28,29,30);(3,4,5,6)(7,9,11,10)(8,13,14,12)(16,21)(17,23)(19,26)(20,27)(24,25)(28,30);(7,10,11,9)(8,13,14,12)(17,24)(20,28)(23,25)(27,30)

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, 6373686);