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C₂×#26262 #6444501

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

Aliases

Subgroups

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6351697);