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C₂²×#2770 #7633526

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

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, 7540722);