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C₂×#37844 #7635325

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

Aliases

Subgroups

8892 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7542521);