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C₂×#23631 #6432164

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

Aliases

Subgroups

3266 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)(17,21)(18,23)(19,22)(20,24)(25,30)(26,28)(27,29);(8,11)(12,14)(15,17)(16,21)(18,26)(19,27)(20,25)(22,29)(23,28)(24,30);(4,6)(7,9,10,13)(8,12,11,14)(16,22)(17,25)(18,20)(21,28)(26,27)(29,30);(15,18,19,20)(16,23,22,24)(17,26,27,25)(21,28,29,30)

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, 6339360);