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C₂×C₃₁×H(3,𝔽₄) #16843459

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 49 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(3,4,7,10)(5,12,13,9)(6,14,16,18)(8,11,17,15);(3,5,7,13)(4,9,10,12)(6,15,16,11)(8,14,17,18);(3,6)(4,5)(7,16)(8,9)(10,13)(11,14)(12,17)(15,18);(3,5)(4,6)(7,13)(8,14)(9,11)(10,16)(12,15)(17,18)

Conjugacy classes & character table

1178 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 2258);