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C₂²×#2748 #7633501

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

Aliases

Subgroups

9122 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540697);