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C₂×#42815 #7641467

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

Aliases

Subgroups

8236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548663);