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C₂²×#3394 #10576691

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

Aliases

Subgroups

7338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483887);