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C₂×#26635 #6439522

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

Aliases

Subgroups

2808 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6346718);