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C₂×#16382 #610890

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

Aliases

Subgroups

5354 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 518086);