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C₂²×#3495 #10585981

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

Aliases

Subgroups

35054 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)(13,14,18,21)(15,16,23,19)(17,25,26,20)(22,27,28,24);(5,6,8,10)(7,9,11,12)(13,15,18,23)(14,19,21,16)(17,22,26,28)(20,27,25,24);(5,7)(6,9)(8,11)(10,12)(13,16)(14,15)(17,24)(18,19)(20,22)(21,23)(25,28)(26,27);(13,15)(14,16)(17,22)(18,23)(19,21)(20,24)(25,27)(26,28);(13,17,18,26)(14,20,21,25)(15,22,23,28)(16,24,19,27)

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, 10493177);