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C₂×#27256 #6440724

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

Aliases

Subgroups

3514 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)(17,27)(18,22)(19,23)(20,30)(21,26)(24,29)(25,28);(3,4)(5,6)(8,11)(12,14)(15,17,20,18,21,19,28,29)(16,22,25,27,26,24,30,23);(4,6)(7,9,10,13)(8,12,11,14)(15,18,28,17,21,29,20,19)(16,23,30,24,26,27,25,22);(8,11)(12,14)(15,19,20,29,21,17,28,18)(16,24,25,23,26,22,30,27)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6347920);