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C₂×#17223 #845037

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

Aliases

Subgroups

3974 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 752233);