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C₂×#23738 #6432415

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

Aliases

Subgroups

3458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6339611);