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C₂×#50166 #7705758

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

Aliases

Subgroups

8690 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7612954);