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C₂×#16741 #611475

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

Aliases

Subgroups

4074 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)(12,14)(15,16,18,20)(17,19,21,22)(23,24,27,28)(25,26,29,30);(3,4,6,5)(8,11)(12,14)(24,28)(25,29);(4,5)(7,8)(9,12)(10,11)(13,14)(15,16)(17,19)(18,20)(21,22)(23,25)(24,26)(27,29)(28,30);(3,5,6,4)(7,9,10,13)(8,12,11,14)(15,17,18,21)(16,19,20,22)(23,26)(24,29)(25,28)(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, 518671);