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C₂×#47841 #7703759

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

Aliases

Subgroups

8344 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7610955);