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C₂²×#2739 #7633518

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

Aliases

Subgroups

7250 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)(13,14,16,18)(15,19,20,17)(21,22)(23,28)(24,25)(26,27);(6,9)(10,11)(13,14,16,18)(15,17,20,19)(21,23,26,24)(22,25,27,28);(5,7,8,12)(6,10,9,11)(13,14)(15,17)(16,18)(19,20)(21,24,26,23)(22,25,27,28);(5,6)(7,10)(8,9)(11,12)(13,15)(14,17)(16,20)(18,19)(21,25)(22,23)(24,27)(26,28)

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, 7540714);