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C₂×#5769 #87184

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 21 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19760);