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C₂×#52006 #7708079

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

Aliases

Subgroups

8458 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7615275);