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C₂×#51317 #7706768

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

Aliases

Subgroups

8436 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

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, 7613964);