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C₂×#25845 #6445731

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

Aliases

Subgroups

3352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6352927);