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C₂×#23810 #6432600

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

Aliases

Subgroups

3514 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339796);