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C₂×#15026 #608107

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

Aliases

Subgroups

5806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 515303);