# Transitive groups downloaded from the LMFDB on 09 November 2024.
# Search link: https://www.lmfdb.org/GaloisGroup/?gal=A4
# Query "{'n': {'$in': [4, 12, 6]}, 'label': {'$in': ['4T4', '12T4', '6T4']}}" returned 3 groups, sorted by degree.
# Each entry in the following data list has the form:
# [Label, Name, Order, Parity, Solvable, Subfields, Low Degree Siblings]
# For more details, see the definitions at the bottom of the file.
"4T4" "$A_4$" 12 1 1 [] [[[[6, 4], 1], [[12, 4], 1]], 47]
"6T4" "$A_4$" 12 1 1 [[[3, 1], 1]] [[[[4, 4], 1], [[12, 4], 1]], 47]
"12T4" "$A_4$" 12 1 1 [[[3, 1], 1], [[4, 4], 1], [[6, 4], 1]] [[[[4, 4], 1], [[6, 4], 1]], 47]
# Label --
# Labels for Galois groups are of the form $\tt{nTt}$ where $n$ is the degree and $t$ is the $T$-number.
#Name (pretty) --
# We describe abstract groups using standard building blocks:
#
# - $C_n$ denotes the cyclic group of order $n$
#
- $D_n$ denotes the dihedral group of order $2n$
#
- $A_n$ denotes the alternating group on $n$ letters
#
- $S_n$ denotes the symmetric group on $n$ letters
#

# Groups $A$ and $B$ may be used to construct a larger group:
# - $A\times B$ for the direct product of $A$ and $B$
# - $A:B$ for the semidirect product of $A$ and $B$ (with normal subgroup $A$)
# - $A.B$ an extension with normal subgroup $A$ and quotient isomorphic to $B$
# - $A\wr B$ for the wreath product of A and B
# Order --
# The **order** of a group is its cardinality as a set.
# Parity --
# A Galois group $G\leq S_n$ has **parity** $1$ if $G\leq A_n$, and $-1$ otherwise.
#Solvable (solv) --
# A group $G$ is **solvable** if there exists a chain of subgroups
# \[ \langle e\rangle =H_0\leq H_1 \leq H_2 \leq \cdots \leq H_n=G\]
# such that for all $i