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C₂×#28127 #6459401

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

Aliases

Subgroups

3148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6366597);