Extensions 1→N→G→Q→1 with N=C₂ and Q=C₂².₅₀C₂⁴

Direct product G=N×Q with N=C₂ and Q=C₂².₅₀C₂⁴

		d	ρ	Label	ID
C₂×C₂².₅₀C₂⁴		64		C2xC2^2.50C2^4	128,2206

Non-split extensions G=N.Q with N=C₂ and Q=C₂².₅₀C₂⁴

extension	φ:Q→Aut N	d	Label	ID
C₂.₁(C₂².₅₀C₂⁴) = C₂³.₂₂₉C₂⁴	central extension (φ=1)	64	C2.1(C2^2.50C2^4)	128,1079
C₂.₂(C₂².₅₀C₂⁴) = C₂³.₂₃₆C₂⁴	central extension (φ=1)	64	C2.2(C2^2.50C2^4)	128,1086
C₂.₃(C₂².₅₀C₂⁴) = C₂³.₂₃₇C₂⁴	central extension (φ=1)	128	C2.3(C2^2.50C2^4)	128,1087
C₂.₄(C₂².₅₀C₂⁴) = C₂³.₂₃₈C₂⁴	central extension (φ=1)	128	C2.4(C2^2.50C2^4)	128,1088
C₂.₅(C₂².₅₀C₂⁴) = C₂³.₂₄₄C₂⁴	central extension (φ=1)	64	C2.5(C2^2.50C2^4)	128,1094
C₂.₆(C₂².₅₀C₂⁴) = C₂³.₂₄₇C₂⁴	central extension (φ=1)	128	C2.6(C2^2.50C2^4)	128,1097
C₂.₇(C₂².₅₀C₂⁴) = C₂⁴.₂₂₀C₂³	central extension (φ=1)	64	C2.7(C2^2.50C2^4)	128,1099
C₂.₈(C₂².₅₀C₂⁴) = C₂³.₂₅₅C₂⁴	central extension (φ=1)	64	C2.8(C2^2.50C2^4)	128,1105
C₂.₉(C₂².₅₀C₂⁴) = C₂³.₃₁₅C₂⁴	central stem extension (φ=1)	64	C2.9(C2^2.50C2^4)	128,1147
C₂.₁₀(C₂².₅₀C₂⁴) = C₂³.₃₂₁C₂⁴	central stem extension (φ=1)	64	C2.10(C2^2.50C2^4)	128,1153
C₂.₁₁(C₂².₅₀C₂⁴) = C₂⁴.₂₆₇C₂³	central stem extension (φ=1)	64	C2.11(C2^2.50C2^4)	128,1171
C₂.₁₂(C₂².₅₀C₂⁴) = C₂³.₃₄₆C₂⁴	central stem extension (φ=1)	128	C2.12(C2^2.50C2^4)	128,1178
C₂.₁₃(C₂².₅₀C₂⁴) = C₂⁴.₂₇₁C₂³	central stem extension (φ=1)	64	C2.13(C2^2.50C2^4)	128,1179
C₂.₁₄(C₂².₅₀C₂⁴) = C₂³.₃₄₈C₂⁴	central stem extension (φ=1)	64	C2.14(C2^2.50C2^4)	128,1180
C₂.₁₅(C₂².₅₀C₂⁴) = C₂⁴.₂₈₅C₂³	central stem extension (φ=1)	64	C2.15(C2^2.50C2^4)	128,1197
C₂.₁₆(C₂².₅₀C₂⁴) = C₂⁴.₂₈₆C₂³	central stem extension (φ=1)	64	C2.16(C2^2.50C2^4)	128,1198
C₂.₁₇(C₂².₅₀C₂⁴) = C₂³.₃₆₉C₂⁴	central stem extension (φ=1)	64	C2.17(C2^2.50C2^4)	128,1201
C₂.₁₈(C₂².₅₀C₂⁴) = C₂³.₃₇₄C₂⁴	central stem extension (φ=1)	64	C2.18(C2^2.50C2^4)	128,1206
C₂.₁₉(C₂².₅₀C₂⁴) = C₂⁴.₂₉₅C₂³	central stem extension (φ=1)	64	C2.19(C2^2.50C2^4)	128,1210
C₂.₂₀(C₂².₅₀C₂⁴) = C₂³.₃₈₅C₂⁴	central stem extension (φ=1)	64	C2.20(C2^2.50C2^4)	128,1217
C₂.₂₁(C₂².₅₀C₂⁴) = C₂³.₃₉₂C₂⁴	central stem extension (φ=1)	64	C2.21(C2^2.50C2^4)	128,1224
C₂.₂₂(C₂².₅₀C₂⁴) = C₂⁴.₃₀₄C₂³	central stem extension (φ=1)	64	C2.22(C2^2.50C2^4)	128,1226
C₂.₂₃(C₂².₅₀C₂⁴) = C₂³.₃₉₆C₂⁴	central stem extension (φ=1)	64	C2.23(C2^2.50C2^4)	128,1228
C₂.₂₄(C₂².₅₀C₂⁴) = C₂⁴.₃₀₈C₂³	central stem extension (φ=1)	64	C2.24(C2^2.50C2^4)	128,1231
C₂.₂₅(C₂².₅₀C₂⁴) = C₂³.₄₀₉C₂⁴	central stem extension (φ=1)	128	C2.25(C2^2.50C2^4)	128,1241
C₂.₂₆(C₂².₅₀C₂⁴) = C₂³.₄₁₂C₂⁴	central stem extension (φ=1)	64	C2.26(C2^2.50C2^4)	128,1244
C₂.₂₇(C₂².₅₀C₂⁴) = C₂³.₄₁₄C₂⁴	central stem extension (φ=1)	128	C2.27(C2^2.50C2^4)	128,1246
C₂.₂₈(C₂².₅₀C₂⁴) = C₂⁴.₃₁₁C₂³	central stem extension (φ=1)	64	C2.28(C2^2.50C2^4)	128,1253
C₂.₂₉(C₂².₅₀C₂⁴) = C₂⁴.₃₁₃C₂³	central stem extension (φ=1)	64	C2.29(C2^2.50C2^4)	128,1255
C₂.₃₀(C₂².₅₀C₂⁴) = C₂³.₄₂₄C₂⁴	central stem extension (φ=1)	128	C2.30(C2^2.50C2^4)	128,1256
C₂.₃₁(C₂².₅₀C₂⁴) = C₂³.₄₂₅C₂⁴	central stem extension (φ=1)	64	C2.31(C2^2.50C2^4)	128,1257
C₂.₃₂(C₂².₅₀C₂⁴) = C₂⁴.₃₁₅C₂³	central stem extension (φ=1)	64	C2.32(C2^2.50C2^4)	128,1259
C₂.₃₃(C₂².₅₀C₂⁴) = C₂³.₄₂₈C₂⁴	central stem extension (φ=1)	128	C2.33(C2^2.50C2^4)	128,1260
C₂.₃₄(C₂².₅₀C₂⁴) = C₂³.₄₃₂C₂⁴	central stem extension (φ=1)	64	C2.34(C2^2.50C2^4)	128,1264
C₂.₃₅(C₂².₅₀C₂⁴) = C₂³.₄₃₃C₂⁴	central stem extension (φ=1)	128	C2.35(C2^2.50C2^4)	128,1265
C₂.₃₆(C₂².₅₀C₂⁴) = C₄².₁₆₆D₄	central stem extension (φ=1)	64	C2.36(C2^2.50C2^4)	128,1270
C₂.₃₇(C₂².₅₀C₂⁴) = C₄².₁₆₈D₄	central stem extension (φ=1)	64	C2.37(C2^2.50C2^4)	128,1277
C₂.₃₈(C₂².₅₀C₂⁴) = C₄².₁₇₀D₄	central stem extension (φ=1)	64	C2.38(C2^2.50C2^4)	128,1279
C₂.₃₉(C₂².₅₀C₂⁴) = C₂⁴.₃₃₂C₂³	central stem extension (φ=1)	64	C2.39(C2^2.50C2^4)	128,1292
C₂.₄₀(C₂².₅₀C₂⁴) = C₄².₁₇₇D₄	central stem extension (φ=1)	128	C2.40(C2^2.50C2^4)	128,1300
C₂.₄₁(C₂².₅₀C₂⁴) = C₄².₃₆Q₈	central stem extension (φ=1)	128	C2.41(C2^2.50C2^4)	128,1302
C₂.₄₂(C₂².₅₀C₂⁴) = C₄².₃₇Q₈	central stem extension (φ=1)	128	C2.42(C2^2.50C2^4)	128,1303
C₂.₄₃(C₂².₅₀C₂⁴) = C₂³.₄₇₃C₂⁴	central stem extension (φ=1)	64	C2.43(C2^2.50C2^4)	128,1305
C₂.₄₄(C₂².₅₀C₂⁴) = C₂⁴.₃₄₁C₂³	central stem extension (φ=1)	64	C2.44(C2^2.50C2^4)	128,1309
C₂.₄₅(C₂².₅₀C₂⁴) = C₄².₁₇₉D₄	central stem extension (φ=1)	128	C2.45(C2^2.50C2^4)	128,1313
C₂.₄₆(C₂².₅₀C₂⁴) = C₂³.₄₈₈C₂⁴	central stem extension (φ=1)	128	C2.46(C2^2.50C2^4)	128,1320
C₂.₄₇(C₂².₅₀C₂⁴) = C₄².₁₈₂D₄	central stem extension (φ=1)	64	C2.47(C2^2.50C2^4)	128,1324
C₂.₄₈(C₂².₅₀C₂⁴) = C₂³.₄₉₄C₂⁴	central stem extension (φ=1)	64	C2.48(C2^2.50C2^4)	128,1326
C₂.₄₉(C₂².₅₀C₂⁴) = C₂³.₄₉₆C₂⁴	central stem extension (φ=1)	64	C2.49(C2^2.50C2^4)	128,1328
C₂.₅₀(C₂².₅₀C₂⁴) = C₄².₁₈₃D₄	central stem extension (φ=1)	64	C2.50(C2^2.50C2^4)	128,1331
C₂.₅₁(C₂².₅₀C₂⁴) = C₄²⋊₂₃D₄	central stem extension (φ=1)	64	C2.51(C2^2.50C2^4)	128,1333
C₂.₅₂(C₂².₅₀C₂⁴) = C₄².₁₈₄D₄	central stem extension (φ=1)	64	C2.52(C2^2.50C2^4)	128,1336
C₂.₅₃(C₂².₅₀C₂⁴) = C₄²⋊₈Q₈	central stem extension (φ=1)	128	C2.53(C2^2.50C2^4)	128,1337
C₂.₅₄(C₂².₅₀C₂⁴) = C₂³.₅₈₉C₂⁴	central stem extension (φ=1)	64	C2.54(C2^2.50C2^4)	128,1421
C₂.₅₅(C₂².₅₀C₂⁴) = C₂³.₆₀₀C₂⁴	central stem extension (φ=1)	64	C2.55(C2^2.50C2^4)	128,1432
C₂.₅₆(C₂².₅₀C₂⁴) = C₂³.₆₁₅C₂⁴	central stem extension (φ=1)	64	C2.56(C2^2.50C2^4)	128,1447
C₂.₅₇(C₂².₅₀C₂⁴) = C₂³.₆₁₆C₂⁴	central stem extension (φ=1)	64	C2.57(C2^2.50C2^4)	128,1448
C₂.₅₈(C₂².₅₀C₂⁴) = C₂³.₆₂₇C₂⁴	central stem extension (φ=1)	64	C2.58(C2^2.50C2^4)	128,1459
C₂.₅₉(C₂².₅₀C₂⁴) = C₂³.₆₄₀C₂⁴	central stem extension (φ=1)	64	C2.59(C2^2.50C2^4)	128,1472
C₂.₆₀(C₂².₅₀C₂⁴) = C₂³.₆₄₅C₂⁴	central stem extension (φ=1)	64	C2.60(C2^2.50C2^4)	128,1477
C₂.₆₁(C₂².₅₀C₂⁴) = C₂³.₆₅₈C₂⁴	central stem extension (φ=1)	128	C2.61(C2^2.50C2^4)	128,1490
C₂.₆₂(C₂².₅₀C₂⁴) = C₂³.₆₅₉C₂⁴	central stem extension (φ=1)	64	C2.62(C2^2.50C2^4)	128,1491
C₂.₆₃(C₂².₅₀C₂⁴) = C₂³.₆₆₂C₂⁴	central stem extension (φ=1)	128	C2.63(C2^2.50C2^4)	128,1494
C₂.₆₄(C₂².₅₀C₂⁴) = C₂³.₆₆₇C₂⁴	central stem extension (φ=1)	128	C2.64(C2^2.50C2^4)	128,1499
C₂.₆₅(C₂².₅₀C₂⁴) = C₂³.₆₇₅C₂⁴	central stem extension (φ=1)	64	C2.65(C2^2.50C2^4)	128,1507
C₂.₆₆(C₂².₅₀C₂⁴) = C₂³.₆₇₆C₂⁴	central stem extension (φ=1)	128	C2.66(C2^2.50C2^4)	128,1508
C₂.₆₇(C₂².₅₀C₂⁴) = C₂³.₆₇₇C₂⁴	central stem extension (φ=1)	64	C2.67(C2^2.50C2^4)	128,1509
C₂.₆₈(C₂².₅₀C₂⁴) = C₂³.₆₈₃C₂⁴	central stem extension (φ=1)	64	C2.68(C2^2.50C2^4)	128,1515
C₂.₆₉(C₂².₅₀C₂⁴) = C₂³.₆₈₆C₂⁴	central stem extension (φ=1)	64	C2.69(C2^2.50C2^4)	128,1518
C₂.₇₀(C₂².₅₀C₂⁴) = C₂³.₆₈₇C₂⁴	central stem extension (φ=1)	64	C2.70(C2^2.50C2^4)	128,1519
C₂.₇₁(C₂².₅₀C₂⁴) = C₂³.₆₈₈C₂⁴	central stem extension (φ=1)	64	C2.71(C2^2.50C2^4)	128,1520
C₂.₇₂(C₂².₅₀C₂⁴) = C₂³.₆₈₉C₂⁴	central stem extension (φ=1)	128	C2.72(C2^2.50C2^4)	128,1521
C₂.₇₃(C₂².₅₀C₂⁴) = C₂³.₆₉₃C₂⁴	central stem extension (φ=1)	64	C2.73(C2^2.50C2^4)	128,1525
C₂.₇₄(C₂².₅₀C₂⁴) = C₂³.₆₉₈C₂⁴	central stem extension (φ=1)	64	C2.74(C2^2.50C2^4)	128,1530
C₂.₇₅(C₂².₅₀C₂⁴) = C₂³.₇₀₀C₂⁴	central stem extension (φ=1)	64	C2.75(C2^2.50C2^4)	128,1532
C₂.₇₆(C₂².₅₀C₂⁴) = C₂³.₇₀₅C₂⁴	central stem extension (φ=1)	128	C2.76(C2^2.50C2^4)	128,1537
C₂.₇₇(C₂².₅₀C₂⁴) = C₂³.₇₀₈C₂⁴	central stem extension (φ=1)	64	C2.77(C2^2.50C2^4)	128,1540
C₂.₇₈(C₂².₅₀C₂⁴) = C₂³.₇₁₀C₂⁴	central stem extension (φ=1)	128	C2.78(C2^2.50C2^4)	128,1542

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Extensions 1→N→G→Q→1 with N=C2 and Q=C22.50C24

Extensions 1→N→G→Q→1 with N=C₂ and Q=C₂².₅₀C₂⁴