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Extensions 1→N→G→Q→1 with N=Dic5 and Q=D6

Direct product G=NxQ with N=Dic5 and Q=D6
dρLabelID
C2xS3xDic5120C2xS3xDic5240,142

Semidirect products G=N:Q with N=Dic5 and Q=D6
extensionφ:Q→Out NdρLabelID
Dic5:1D6 = S3xC5:D4φ: D6/S3 → C2 ⊆ Out Dic5604Dic5:1D6240,150
Dic5:2D6 = D10:D6φ: D6/S3 → C2 ⊆ Out Dic5604+Dic5:2D6240,151
Dic5:3D6 = D5xD12φ: D6/C6 → C2 ⊆ Out Dic5604+Dic5:3D6240,136
Dic5:4D6 = C2xC5:D12φ: D6/C6 → C2 ⊆ Out Dic5120Dic5:4D6240,147
Dic5:5D6 = C4xS3xD5φ: trivial image604Dic5:5D6240,135
Dic5:6D6 = C2xD30.C2φ: trivial image120Dic5:6D6240,144

Non-split extensions G=N.Q with N=Dic5 and Q=D6
extensionφ:Q→Out NdρLabelID
Dic5.1D6 = S3xDic10φ: D6/S3 → C2 ⊆ Out Dic51204-Dic5.1D6240,128
Dic5.2D6 = D12:D5φ: D6/S3 → C2 ⊆ Out Dic51204Dic5.2D6240,129
Dic5.3D6 = D60:C2φ: D6/S3 → C2 ⊆ Out Dic51204+Dic5.3D6240,130
Dic5.4D6 = D15:Q8φ: D6/S3 → C2 ⊆ Out Dic51204Dic5.4D6240,131
Dic5.5D6 = Dic5.D6φ: D6/S3 → C2 ⊆ Out Dic51204Dic5.5D6240,140
Dic5.6D6 = C30.C23φ: D6/S3 → C2 ⊆ Out Dic51204-Dic5.6D6240,141
Dic5.7D6 = S3xC5:C8φ: D6/S3 → C2 ⊆ Out Dic51208-Dic5.7D6240,98
Dic5.8D6 = D15:C8φ: D6/S3 → C2 ⊆ Out Dic51208+Dic5.8D6240,99
Dic5.9D6 = D6.F5φ: D6/S3 → C2 ⊆ Out Dic51208-Dic5.9D6240,100
Dic5.10D6 = Dic3.F5φ: D6/S3 → C2 ⊆ Out Dic51208+Dic5.10D6240,101
Dic5.11D6 = D5xDic6φ: D6/C6 → C2 ⊆ Out Dic51204-Dic5.11D6240,125
Dic5.12D6 = D6.D10φ: D6/C6 → C2 ⊆ Out Dic51204Dic5.12D6240,132
Dic5.13D6 = Dic3.D10φ: D6/C6 → C2 ⊆ Out Dic51204Dic5.13D6240,143
Dic5.14D6 = C2xC15:Q8φ: D6/C6 → C2 ⊆ Out Dic5240Dic5.14D6240,148
Dic5.15D6 = C60.C4φ: D6/C6 → C2 ⊆ Out Dic51204Dic5.15D6240,118
Dic5.16D6 = C12.F5φ: D6/C6 → C2 ⊆ Out Dic51204Dic5.16D6240,119
Dic5.17D6 = C2xC15:C8φ: D6/C6 → C2 ⊆ Out Dic5240Dic5.17D6240,122
Dic5.18D6 = C15:8M4(2)φ: D6/C6 → C2 ⊆ Out Dic51204Dic5.18D6240,123
Dic5.19D6 = D12:5D5φ: trivial image1204-Dic5.19D6240,133
Dic5.20D6 = C12.28D10φ: trivial image1204+Dic5.20D6240,134

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