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C₂×#24126 #6448571

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

Aliases

Subgroups

3726 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)(9,13)(10,11)(12,14)(15,16)(17,21)(18,20)(19,22)(23,30)(24,27)(25,28)(26,29);(8,11)(12,13)(16,20)(17,23)(19,25)(21,29)(24,26)(27,30);(4,6)(15,17,18,24)(16,21,20,27)(19,26,25,23)(22,29,28,30);(7,9,10,14)(8,12,11,13)(16,20)(21,27)(22,28)(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, 6355767);