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C₂²×#1494 #6342965

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

Aliases

Subgroups

3734 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 28 points:

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

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, 6250161);