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C₂×#24074 #6452894

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

Aliases

Subgroups

3442 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6360090);