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C₂×#28192 #6463760

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

Aliases

Subgroups

2238 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)(17,20)(18,22)(19,21)(23,27)(24,28)(25,30)(26,29);(8,11)(12,13)(15,17,23,24,19,26,18,25)(16,20,27,28,21,29,22,30);(4,6)(17,24)(18,23)(20,28)(22,27)(25,26)(29,30);(7,9,10,14)(8,12,11,13)(16,21)(20,29)(22,27)(28,30)

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, 6370956);