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C₂²×#3307 #10576259

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

Aliases

Subgroups

8134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

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, 10483455);