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C₂×#40600 #7639333

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

Aliases

Subgroups

8690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7546529);