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C₂²×#3219 #10575492

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

Aliases

Subgroups

8154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482688);