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C₂³×C₂²⋊D₇ #90622

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1362 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 17 points:

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

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1384);