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C₂×#16416 #610927

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

Aliases

Subgroups

4310 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518123);