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C₂×#28212 #6463815

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

Aliases

Subgroups

2226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(7,8,10,11)(9,13,14,12)(15,16,19,23)(17,20,24,28)(18,21,26,22)(25,29,30,27);(3,4,5,6)(8,11)(12,13)(15,17)(16,20)(18,25)(19,24)(21,29)(22,27)(23,28)(26,30);(4,6)(16,21)(17,24)(18,26)(20,27)(22,23)(28,29);(7,9,10,14)(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, 6371011);