# Checker for HN.2

# Check orders from the definition
chor 1 2
chor 2 5
mu 1 2 3
chor 3 42

# Find a 2A element c by powering up an element of order 60
pwr 4 3 4
mu 2 2 5
mu 3 5 6
mu 6 4 7
chor 7 60
pwr 30 7 8

# (c,b) is a (2A,5,22) pair. To show that b is in 5A, we test
# whether cb^2(cb)^3 has order 22
mu 8 2 9
chor 9 22
mu 9 2 10
pwr 3 9 11
mu 10 11 12
chor 12 22