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C₂×#26565 #6439291

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

Aliases

Subgroups

2640 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)(17,25)(18,23)(19,21)(20,24)(22,28)(26,29)(27,30);(3,4)(5,6)(16,21)(18,19)(22,29)(23,24)(25,30)(26,27);(4,6)(8,11)(12,14)(15,17,20,28)(16,22,24,25)(18,26,19,27)(21,29,23,30);(7,9,10,13)(8,12,11,14)(15,18)(17,26)(19,20)(21,23)(27,28)(29,30)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6346487);