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C₂²×#3125 #10575084

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

Aliases

Subgroups

7938 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482280);