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C₂²×#3153 #10575238

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

Aliases

Subgroups

13370 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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, 10482434);