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C₂²×#3135 #10575197

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

Aliases

Subgroups

8114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482393);