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C₂²×#3396 #10576692

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

Aliases

Subgroups

7554 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)(13,14,18,21)(15,19,17,25)(16,23,24,27)(20,26,28,22);(5,6,9,10)(7,11,8,12)(13,15,18,17)(14,19,21,25)(16,22,24,26)(20,27,28,23);(5,7,9,8)(6,11,10,12)(13,16,18,24)(14,20,21,28)(15,22,17,26)(19,27,25,23);(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, 10483888);