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C₂²×#3136 #10575198

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

Aliases

Subgroups

8474 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)(14,18)(15,21)(16,23)(19,26)(20,25)(22,27);(6,9)(10,12)(13,14,16,18,17,20,23,25)(15,19,21,24,22,26,27,28);(5,7,8,11)(6,10,9,12)(13,15,16,21,17,22,23,27)(14,19,18,24,20,26,25,28);(14,20)(18,25)(19,26)(24,28)

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, 10482394);