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C₂×#30496 #7500915

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

Aliases

Subgroups

3296 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7408111);