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C₂×#23632 #6432159

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

Aliases

Subgroups

3626 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339355);