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C₂×#15015 #608094

• 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);(4,6)(7,8)(9,11)(10,13)(12,14)(15,16,18,20)(17,21,22,19)(23,24,27,26)(25,29,30,28);(8,9)(12,13)(15,16,18,20)(17,19,22,21)(23,25)(24,28)(26,29)(27,30);(3,4)(5,6)(7,9,11,8)(10,13,14,12)(15,16)(17,19)(18,20)(21,22)(23,26,27,24)(25,29,30,28);(7,10)(8,12)(9,13)(11,14)(15,17)(16,19)(18,22)(20,21)(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, 515290);