Extensions 1→N→G→Q→1 with N=He3 and Q=C15

Direct product G=N×Q with N=He3 and Q=C15
dρLabelID
C15×He3135C15xHe3405,12

Semidirect products G=N:Q with N=He3 and Q=C15
extensionφ:Q→Out NdρLabelID
He31C15 = C5×C3≀C3φ: C15/C5C3 ⊆ Out He3453He3:1C15405,7
He32C15 = C5×He3⋊C3φ: C15/C5C3 ⊆ Out He31353He3:2C15405,9

Non-split extensions G=N.Q with N=He3 and Q=C15
extensionφ:Q→Out NdρLabelID
He3.C15 = C5×He3.C3φ: C15/C5C3 ⊆ Out He31353He3.C15405,8
He3.2C15 = C5×C9○He3φ: trivial image1353He3.2C15405,14

׿
×
𝔽