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C₂²×D₅₂ #88247

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 21 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 214);