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C₂×#17152 #844929

• 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)(7,8,11,9)(10,13,14,12)(15,16)(17,20)(18,19)(21,22)(23,24)(25,27)(26,29)(28,30);(8,9)(10,14)(16,18)(20,22)(23,25,26,30)(24,27,29,28);(7,9,11,8)(10,12,14,13)(15,17,19,21)(16,20,18,22)(23,25)(24,28)(26,30)(27,29);(3,4)(5,6)(7,10,11,14)(8,12,9,13)(15,18,19,16)(17,20,21,22)(23,24)(25,28)(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, 752125);