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C₂×#47954 #7703914

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

Aliases

Subgroups

8572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7611110);