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C₂²×#3493 #10585954

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

Aliases

Subgroups

35378 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10493150);