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Degree	Signature	Discriminant	Root discriminant	Galois root discriminant

Ramified prime count	Ramified	Unramified primes	Maximum ramified prime	Galois group

Class group structure	Class number	Regulator	Intermediate field	Field is

Narrow class group	Narrow class number	Relative class number	CM field	$p$-adic completions

Monogenic	Index	Ines. \(p\)	Minimal sibling	Unit signature rank

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Narrow class group	Unit group torsion	Unit group rank	Regulator	Unit signature rank	Max $p$
27.27.663...849.1	$x^{27} - 189 x^{25} - 216 x^{24} + 13365 x^{23} + 26451 x^{22} - 435558 x^{21} - 1092879 x^{20} + 6736293 x^{19} + 18444710 x^{18} - 51315120 x^{17} - 141089958 x^{16} + 209139921 x^{15} + 559621872 x^{14} - 467867826 x^{13} - 1233307335 x^{12} + 539126172 x^{11} + 1534353237 x^{10} - 236530428 x^{9} - 1036028880 x^{8} - 52867863 x^{7} + 340586379 x^{6} + 59598450 x^{5} - 46439829 x^{4} - 10405386 x^{3} + 2275830 x^{2} + 512244 x - 15317$	$27$	(27, 0)	$3^{66}\cdot 337^{12}$	$2$	$194.84419325440825$				?	$\He_3.S_3$ (as 27T41)	trivial	$[2, 2, 2, 2]$	$2$	$26$	$26755878363303130000000$	$23$	$337$

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