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C₂×#20365 #6369772

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

Aliases

Subgroups

3210 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)(15,16,18,22,19,21,25,28)(17,20,24,27,23,26,29,30);(3,4,5,6)(8,11)(12,14)(15,17)(16,20)(18,24)(19,23)(21,26)(22,27)(25,29)(28,30);(7,9,10,13)(8,12,11,14)(17,23)(20,26)(24,29)(27,30);(16,21)(20,26)(22,28)(27,30)

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276968);