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C₂×#48785 #7704558

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

Aliases

Subgroups

8840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7611754);