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C₂×#16498 #611017

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

Aliases

Subgroups

3786 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)(15,16,18,20)(17,19,21,22)(24,27)(25,29);(8,9)(12,13)(17,21)(19,22)(23,24,26,27)(25,28,29,30);(7,9,11,8)(10,12,14,13)(15,17)(16,19)(18,21)(20,22)(23,24)(25,30)(26,27)(28,29);(3,4)(5,6)(7,10,11,14)(8,12,9,13)(15,16)(17,19)(18,20)(21,22)(23,25)(24,28)(26,29)(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, 518213);