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C₂×#23996 #6451860

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

Aliases

Subgroups

4700 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 18 points:

(1,2);(3,4)(5,8)(6,9)(7,10)(11,13)(12,17)(14,16)(15,18);(3,4)(5,11,13,8)(6,9)(7,10)(12,17,18,15)(14,16);(3,5)(4,8)(6,12)(7,13)(9,15)(10,11)(14,18)(16,17);(3,6)(4,9)(5,12)(7,14)(8,15)(10,16)(11,17)(13,18)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6359056);