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C₂×#15205 #608504

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

Aliases

Subgroups

4758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(15,16,18,20)(17,21,22,19)(23,24,27,25)(26,29,30,28);(8,11)(12,14)(24,25)(28,29);(3,4)(5,6)(7,8)(9,12)(10,11)(13,14)(15,16)(17,19)(18,20)(21,22)(23,25,27,24)(26,29,30,28);(7,9,10,13)(8,12,11,14)(15,17,18,22)(16,19,20,21)(23,26)(24,28)(25,29)(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, 515700);