# Extensions 1→N→G→Q→1 with N=C56 and Q=C23

Direct product G=N×Q with N=C56 and Q=C23
dρLabelID
C23×C56448C2^3xC56448,1348

Semidirect products G=N:Q with N=C56 and Q=C23
extensionφ:Q→Aut NdρLabelID
C56⋊C23 = D7×C8⋊C22φ: C23/C1C23 ⊆ Aut C56568+C56:C2^3448,1225
C562C23 = C2×C8⋊D14φ: C23/C2C22 ⊆ Aut C56112C56:2C2^3448,1199
C563C23 = C2×D7×D8φ: C23/C2C22 ⊆ Aut C56112C56:3C2^3448,1207
C564C23 = C2×D56⋊C2φ: C23/C2C22 ⊆ Aut C56112C56:4C2^3448,1212
C565C23 = C2×D8⋊D7φ: C23/C2C22 ⊆ Aut C56112C56:5C2^3448,1208
C566C23 = C2×D7×SD16φ: C23/C2C22 ⊆ Aut C56112C56:6C2^3448,1211
C567C23 = C2×D7×M4(2)φ: C23/C2C22 ⊆ Aut C56112C56:7C2^3448,1196
C568C23 = C14×C8⋊C22φ: C23/C2C22 ⊆ Aut C56112C56:8C2^3448,1356
C569C23 = C22×D56φ: C23/C22C2 ⊆ Aut C56224C56:9C2^3448,1193
C5610C23 = C22×C56⋊C2φ: C23/C22C2 ⊆ Aut C56224C56:10C2^3448,1192
C5611C23 = D7×C22×C8φ: C23/C22C2 ⊆ Aut C56224C56:11C2^3448,1189
C5612C23 = C22×C8⋊D7φ: C23/C22C2 ⊆ Aut C56224C56:12C2^3448,1190
C5613C23 = D8×C2×C14φ: C23/C22C2 ⊆ Aut C56224C56:13C2^3448,1352
C5614C23 = SD16×C2×C14φ: C23/C22C2 ⊆ Aut C56224C56:14C2^3448,1353
C5615C23 = M4(2)×C2×C14φ: C23/C22C2 ⊆ Aut C56224C56:15C2^3448,1349

Non-split extensions G=N.Q with N=C56 and Q=C23
extensionφ:Q→Aut NdρLabelID
C56.1C23 = SD16⋊D14φ: C23/C1C23 ⊆ Aut C561128-C56.1C2^3448,1226
C56.2C23 = D85D14φ: C23/C1C23 ⊆ Aut C561128+C56.2C2^3448,1227
C56.3C23 = D86D14φ: C23/C1C23 ⊆ Aut C561128-C56.3C2^3448,1228
C56.4C23 = D7×C8.C22φ: C23/C1C23 ⊆ Aut C561128-C56.4C2^3448,1229
C56.5C23 = D56⋊C22φ: C23/C1C23 ⊆ Aut C561128+C56.5C2^3448,1230
C56.6C23 = C56.C23φ: C23/C1C23 ⊆ Aut C561128+C56.6C2^3448,1231
C56.7C23 = D28.44D4φ: C23/C1C23 ⊆ Aut C562248-C56.7C2^3448,1232
C56.8C23 = C2×C8.D14φ: C23/C2C22 ⊆ Aut C56224C56.8C2^3448,1200
C56.9C23 = C56.9C23φ: C23/C2C22 ⊆ Aut C561124C56.9C2^3448,1201
C56.10C23 = D4.11D28φ: C23/C2C22 ⊆ Aut C561124C56.10C2^3448,1204
C56.11C23 = D4.12D28φ: C23/C2C22 ⊆ Aut C561124+C56.11C2^3448,1205
C56.12C23 = D4.13D28φ: C23/C2C22 ⊆ Aut C562244-C56.12C2^3448,1206
C56.13C23 = D7×D16φ: C23/C2C22 ⊆ Aut C561124+C56.13C2^3448,444
C56.14C23 = D8⋊D14φ: C23/C2C22 ⊆ Aut C561124C56.14C2^3448,445
C56.15C23 = D163D7φ: C23/C2C22 ⊆ Aut C562244-C56.15C2^3448,446
C56.16C23 = D7×SD32φ: C23/C2C22 ⊆ Aut C561124C56.16C2^3448,447
C56.17C23 = D112⋊C2φ: C23/C2C22 ⊆ Aut C561124+C56.17C2^3448,448
C56.18C23 = SD32⋊D7φ: C23/C2C22 ⊆ Aut C562244-C56.18C2^3448,449
C56.19C23 = SD323D7φ: C23/C2C22 ⊆ Aut C562244C56.19C2^3448,450
C56.20C23 = D7×Q32φ: C23/C2C22 ⊆ Aut C562244-C56.20C2^3448,451
C56.21C23 = Q32⋊D7φ: C23/C2C22 ⊆ Aut C562244C56.21C2^3448,452
C56.22C23 = Q323D7φ: C23/C2C22 ⊆ Aut C562244+C56.22C2^3448,453
C56.23C23 = C2×C7⋊D16φ: C23/C2C22 ⊆ Aut C56224C56.23C2^3448,680
C56.24C23 = D8.D14φ: C23/C2C22 ⊆ Aut C561124C56.24C2^3448,681
C56.25C23 = C2×D8.D7φ: C23/C2C22 ⊆ Aut C56224C56.25C2^3448,682
C56.26C23 = C2×C7⋊SD32φ: C23/C2C22 ⊆ Aut C56224C56.26C2^3448,712
C56.27C23 = Q16.D14φ: C23/C2C22 ⊆ Aut C562244C56.27C2^3448,713
C56.28C23 = C2×C7⋊Q32φ: C23/C2C22 ⊆ Aut C56448C56.28C2^3448,714
C56.29C23 = Q16⋊D14φ: C23/C2C22 ⊆ Aut C561124+C56.29C2^3448,727
C56.30C23 = C56.30C23φ: C23/C2C22 ⊆ Aut C562244C56.30C2^3448,728
C56.31C23 = C56.31C23φ: C23/C2C22 ⊆ Aut C562244-C56.31C2^3448,729
C56.32C23 = C2×D83D7φ: C23/C2C22 ⊆ Aut C56224C56.32C2^3448,1209
C56.33C23 = C2×D7×Q16φ: C23/C2C22 ⊆ Aut C56224C56.33C2^3448,1216
C56.34C23 = C2×Q8.D14φ: C23/C2C22 ⊆ Aut C56224C56.34C2^3448,1218
C56.35C23 = C2×SD16⋊D7φ: C23/C2C22 ⊆ Aut C56224C56.35C2^3448,1213
C56.36C23 = D28.29D4φ: C23/C2C22 ⊆ Aut C561124C56.36C2^3448,1215
C56.37C23 = D810D14φ: C23/C2C22 ⊆ Aut C561124C56.37C2^3448,1221
C56.38C23 = D815D14φ: C23/C2C22 ⊆ Aut C561124+C56.38C2^3448,1222
C56.39C23 = D8.10D14φ: C23/C2C22 ⊆ Aut C562244-C56.39C2^3448,1224
C56.40C23 = D813D14φ: C23/C2C22 ⊆ Aut C561124C56.40C2^3448,1210
C56.41C23 = C2×Q16⋊D7φ: C23/C2C22 ⊆ Aut C56224C56.41C2^3448,1217
C56.42C23 = D28.30D4φ: C23/C2C22 ⊆ Aut C562244C56.42C2^3448,1219
C56.43C23 = D811D14φ: C23/C2C22 ⊆ Aut C561124C56.43C2^3448,1223
C56.44C23 = C2×SD163D7φ: C23/C2C22 ⊆ Aut C56224C56.44C2^3448,1214
C56.45C23 = D7×C4○D8φ: C23/C2C22 ⊆ Aut C561124C56.45C2^3448,1220
C56.46C23 = C2×D28.C4φ: C23/C2C22 ⊆ Aut C56224C56.46C2^3448,1197
C56.47C23 = C28.70C24φ: C23/C2C22 ⊆ Aut C561124C56.47C2^3448,1198
C56.48C23 = D7×C8○D4φ: C23/C2C22 ⊆ Aut C561124C56.48C2^3448,1202
C56.49C23 = C56.49C23φ: C23/C2C22 ⊆ Aut C561124C56.49C2^3448,1203
C56.50C23 = C14×C8.C22φ: C23/C2C22 ⊆ Aut C56224C56.50C2^3448,1357
C56.51C23 = C7×D8⋊C22φ: C23/C2C22 ⊆ Aut C561124C56.51C2^3448,1358
C56.52C23 = C7×D4○D8φ: C23/C2C22 ⊆ Aut C561124C56.52C2^3448,1359
C56.53C23 = C7×D4○SD16φ: C23/C2C22 ⊆ Aut C561124C56.53C2^3448,1360
C56.54C23 = C7×Q8○D8φ: C23/C2C22 ⊆ Aut C562244C56.54C2^3448,1361
C56.55C23 = C2×D112φ: C23/C22C2 ⊆ Aut C56224C56.55C2^3448,436
C56.56C23 = C2×C112⋊C2φ: C23/C22C2 ⊆ Aut C56224C56.56C2^3448,437
C56.57C23 = D1127C2φ: C23/C22C2 ⊆ Aut C562242C56.57C2^3448,438
C56.58C23 = C2×Dic56φ: C23/C22C2 ⊆ Aut C56448C56.58C2^3448,439
C56.59C23 = C16⋊D14φ: C23/C22C2 ⊆ Aut C561124+C56.59C2^3448,442
C56.60C23 = C16.D14φ: C23/C22C2 ⊆ Aut C562244-C56.60C2^3448,443
C56.61C23 = C22×Dic28φ: C23/C22C2 ⊆ Aut C56448C56.61C2^3448,1195
C56.62C23 = C2×D567C2φ: C23/C22C2 ⊆ Aut C56224C56.62C2^3448,1194
C56.63C23 = D7×C2×C16φ: C23/C22C2 ⊆ Aut C56224C56.63C2^3448,433
C56.64C23 = C2×C16⋊D7φ: C23/C22C2 ⊆ Aut C56224C56.64C2^3448,434
C56.65C23 = D28.4C8φ: C23/C22C2 ⊆ Aut C562242C56.65C2^3448,435
C56.66C23 = D7×M5(2)φ: C23/C22C2 ⊆ Aut C561124C56.66C2^3448,440
C56.67C23 = C16.12D14φ: C23/C22C2 ⊆ Aut C562244C56.67C2^3448,441
C56.68C23 = C22×C7⋊C16φ: C23/C22C2 ⊆ Aut C56448C56.68C2^3448,630
C56.69C23 = C2×C28.C8φ: C23/C22C2 ⊆ Aut C56224C56.69C2^3448,631
C56.70C23 = C56.70C23φ: C23/C22C2 ⊆ Aut C562244C56.70C2^3448,674
C56.71C23 = C2×D28.2C4φ: C23/C22C2 ⊆ Aut C56224C56.71C2^3448,1191
C56.72C23 = C14×D16φ: C23/C22C2 ⊆ Aut C56224C56.72C2^3448,913
C56.73C23 = C14×SD32φ: C23/C22C2 ⊆ Aut C56224C56.73C2^3448,914
C56.74C23 = C14×Q32φ: C23/C22C2 ⊆ Aut C56448C56.74C2^3448,915
C56.75C23 = C7×C4○D16φ: C23/C22C2 ⊆ Aut C562242C56.75C2^3448,916
C56.76C23 = C7×C16⋊C22φ: C23/C22C2 ⊆ Aut C561124C56.76C2^3448,917
C56.77C23 = C7×Q32⋊C2φ: C23/C22C2 ⊆ Aut C562244C56.77C2^3448,918
C56.78C23 = Q16×C2×C14φ: C23/C22C2 ⊆ Aut C56448C56.78C2^3448,1354
C56.79C23 = C14×C4○D8φ: C23/C22C2 ⊆ Aut C56224C56.79C2^3448,1355
C56.80C23 = C14×C8○D4φ: C23/C22C2 ⊆ Aut C56224C56.80C2^3448,1350
C56.81C23 = C7×Q8○M4(2)φ: C23/C22C2 ⊆ Aut C561124C56.81C2^3448,1351
C56.82C23 = C14×M5(2)central extension (φ=1)224C56.82C2^3448,911
C56.83C23 = C7×D4○C16central extension (φ=1)2242C56.83C2^3448,912

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