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C₂×#44513 #7668776

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

Aliases

Subgroups

8578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7575972);