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C₂×#26343 #6439154

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

Aliases

Subgroups

2532 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);(4,6)(7,9,11,10)(8,12,13,14)(15,16,20,23)(17,24,26,29)(18,22,19,27)(21,28,30,25);(7,10,11,9)(8,12,13,14)(15,17,20,26)(16,21,23,30)(18,25,19,28)(22,29,27,24);(4,6)(15,18,20,19)(16,22,23,27)(17,25,26,28)(21,29,30,24)

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, 6346350);