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C₂²×#3524 #10585970

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

Aliases

Subgroups

35014 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493166);