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C₂×#25396 #6444349

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

Aliases

Subgroups

3626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6351545);