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C₂×#28188 #6463757

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

Aliases

Subgroups

2454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6370953);