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C₂²×#2786 #7633544

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

Aliases

Subgroups

8294 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)(8,9)(10,12)(13,14,17,18)(15,19,20,16)(21,22)(23,27)(24,26)(25,28);(6,9)(7,12)(13,15,17,20)(14,16,18,19)(21,22,24,26)(23,25,28,27);(5,6)(7,10)(8,9)(11,12)(13,15)(14,16)(17,20)(18,19)(21,23)(22,25)(24,28)(26,27);(5,7,8,12)(6,10,9,11)(13,16)(14,15)(17,19)(18,20)(21,22)(23,25)(24,26)(27,28)

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, 7540740);