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C₂×#25940 #6447672

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

Aliases

Subgroups

3546 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)(15,16,19,22)(17,23,25,30)(18,26,27,21)(20,28,29,24);(7,9,11,10)(8,12,14,13)(17,24)(18,27)(20,23)(21,26)(25,28)(29,30);(3,4,5,6)(7,9,11,10)(8,13,14,12)(15,17,18,24,19,25,27,28)(16,20,21,23,22,29,26,30);(7,10,11,9)(8,13,14,12)(17,25)(20,29)(23,30)(24,28)

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, 6354868);