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C₂×#37847 #7635326

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

Aliases

Subgroups

8860 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)(16,20)(17,23)(22,27)(24,29);(9,14)(10,13)(15,16,19,20)(17,21,23,26)(18,22,25,27)(24,28,29,30);(3,4)(5,6)(7,9)(8,10)(11,14)(12,13)(15,16)(17,21)(18,22)(19,20)(23,26)(24,28)(25,27)(29,30);(15,17,19,23)(16,21,20,26)(18,24,25,29)(22,28,27,30);(7,10)(8,9)(11,13)(12,14)(15,18,19,25)(16,22,20,27)(17,24,23,29)(21,28,26,30)

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, 7542522);