Finite Group Databasebeta

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Q₈×#235 #85816

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1068 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 19 points:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18392);