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C₂×#14896 #607892

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

Aliases

Subgroups

4050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 515088);