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C₂²×#3518 #10585969

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

Aliases

Subgroups

34646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493165);