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C₂×#23582 #6432024

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

Aliases

Subgroups

3838 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)(17,22)(18,27)(19,24)(20,29)(21,25)(23,28)(26,30);(3,4)(5,6)(8,11)(12,14)(15,17)(16,22)(18,21)(19,28)(20,26)(23,24)(25,27)(29,30);(4,6)(15,18,21,17)(16,23,25,30)(19,28,20,26)(22,29,27,24);(7,9,10,13)(8,12,11,14)(15,19,21,20)(16,24,25,29)(17,26,18,28)(22,30,27,23)

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, 6339220);