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C₄×Q₈×D₇ #90262

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 19 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1024);