Extensions 1→N→G→Q→1 with N=C4xC56 and Q=C2

Direct product G=NxQ with N=C4xC56 and Q=C2
dρLabelID
C2xC4xC56448C2xC4xC56448,810

Semidirect products G=N:Q with N=C4xC56 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C4xC56):1C2 = C4.17D56φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):1C2448,16
(C4xC56):2C2 = C7xD4:C8φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):2C2448,129
(C4xC56):3C2 = C42.282D14φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):3C2448,219
(C4xC56):4C2 = C42.243D14φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):4C2448,224
(C4xC56):5C2 = C4.5D56φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):5C2448,228
(C4xC56):6C2 = C42.264D14φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):6C2448,231
(C4xC56):7C2 = C7xC42.12C4φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):7C2448,839
(C4xC56):8C2 = C7xC42.7C22φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):8C2448,841
(C4xC56):9C2 = D4xC56φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):9C2448,842
(C4xC56):10C2 = C7xC4.4D8φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):10C2448,894
(C4xC56):11C2 = C7xC42.78C22φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):11C2448,896
(C4xC56):12C2 = C4xD56φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):12C2448,226
(C4xC56):13C2 = C28:4D8φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):13C2448,229
(C4xC56):14C2 = C8.8D28φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):14C2448,230
(C4xC56):15C2 = D56:11C4φ: C2/C1C2 ⊆ Aut C4xC561122(C4xC56):15C2448,234
(C4xC56):16C2 = C4xC56:C2φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):16C2448,225
(C4xC56):17C2 = C8:5D28φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):17C2448,227
(C4xC56):18C2 = D7xC4xC8φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):18C2448,218
(C4xC56):19C2 = C8xD28φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):19C2448,220
(C4xC56):20C2 = C4xC8:D7φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):20C2448,221
(C4xC56):21C2 = C8:6D28φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):21C2448,222
(C4xC56):22C2 = D14.C42φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):22C2448,223
(C4xC56):23C2 = D8xC28φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):23C2448,845
(C4xC56):24C2 = C7xC8:4D4φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):24C2448,901
(C4xC56):25C2 = C7xC8.12D4φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):25C2448,903
(C4xC56):26C2 = C7xC8oD8φ: C2/C1C2 ⊆ Aut C4xC561122(C4xC56):26C2448,851
(C4xC56):27C2 = SD16xC28φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):27C2448,846
(C4xC56):28C2 = C7xC8:5D4φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):28C2448,900
(C4xC56):29C2 = M4(2)xC28φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):29C2448,812
(C4xC56):30C2 = C7xC8o2M4(2)φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):30C2448,813
(C4xC56):31C2 = C7xC8:6D4φ: C2/C1C2 ⊆ Aut C4xC56224(C4xC56):31C2448,844

Non-split extensions G=N.Q with N=C4xC56 and Q=C2
extensionφ:Q→Aut NdρLabelID
(C4xC56).1C2 = C42.279D14φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).1C2448,11
(C4xC56).2C2 = C4.8Dic28φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).2C2448,13
(C4xC56).3C2 = C7xQ8:C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).3C2448,130
(C4xC56).4C2 = C7xC4:C16φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).4C2448,167
(C4xC56).5C2 = C28.14Q16φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).5C2448,215
(C4xC56).6C2 = Q8xC56φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).6C2448,853
(C4xC56).7C2 = C7xC4.SD16φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).7C2448,895
(C4xC56).8C2 = C56:1C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).8C2448,15
(C4xC56).9C2 = C56:8Q8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).9C2448,216
(C4xC56).10C2 = C4xDic28φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).10C2448,232
(C4xC56).11C2 = C28:4Q16φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).11C2448,233
(C4xC56).12C2 = C56.13Q8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).12C2448,217
(C4xC56).13C2 = C56.16Q8φ: C2/C1C2 ⊆ Aut C4xC561122(C4xC56).13C2448,20
(C4xC56).14C2 = C56:2C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).14C2448,14
(C4xC56).15C2 = C56:9Q8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).15C2448,214
(C4xC56).16C2 = C8xC7:C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).16C2448,10
(C4xC56).17C2 = C56:C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).17C2448,12
(C4xC56).18C2 = C4xC7:C16φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).18C2448,17
(C4xC56).19C2 = C56.C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).19C2448,18
(C4xC56).20C2 = C28:C16φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).20C2448,19
(C4xC56).21C2 = C8xDic14φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).21C2448,212
(C4xC56).22C2 = C56:11Q8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).22C2448,213
(C4xC56).23C2 = C7xC8:1C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).23C2448,139
(C4xC56).24C2 = Q16xC28φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).24C2448,847
(C4xC56).25C2 = C7xC4:Q16φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).25C2448,902
(C4xC56).26C2 = C7xC8:2Q8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).26C2448,908
(C4xC56).27C2 = C7xC8.5Q8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).27C2448,907
(C4xC56).28C2 = C7xC8.C8φ: C2/C1C2 ⊆ Aut C4xC561122(C4xC56).28C2448,168
(C4xC56).29C2 = C7xC8:2C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).29C2448,138
(C4xC56).30C2 = C7xC8:3Q8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).30C2448,906
(C4xC56).31C2 = C7xC8:C8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).31C2448,126
(C4xC56).32C2 = C7xC16:5C4φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).32C2448,150
(C4xC56).33C2 = C7xC8:4Q8φ: C2/C1C2 ⊆ Aut C4xC56448(C4xC56).33C2448,854

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