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C₂×#28126 #6459397

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

Aliases

Subgroups

3620 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)(17,20)(18,21)(19,23)(22,26)(24,28)(25,27)(29,30);(3,4,5,6)(7,9,10,14)(8,11,12,13)(15,17)(16,20)(18,25)(19,24)(21,27)(22,29)(23,28)(26,30);(4,6)(16,21)(18,26)(20,27)(22,23)(25,30)(28,29);(8,12)(11,13)(17,24)(20,28)(25,30)(27,29)

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, 6366593);