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C₂²×#1488 #6342913

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

Aliases

Subgroups

4398 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6250109);