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C₂×#26346 #6439144

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

Aliases

Subgroups

2446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6346340);