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C₂×#26127 #6438501

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

Aliases

Subgroups

2678 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)(9,12)(10,14)(11,13);(4,6)(7,9,11,10)(8,12,13,14)(15,16)(17,24)(18,22)(19,27)(20,23)(21,25)(26,29)(28,30);(7,10,11,9)(8,12,13,14)(15,17)(16,21)(18,25)(19,28)(20,26)(22,29)(23,30)(24,27);(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, 6345697);