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C₂×#4685 #78453

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11029);