Extensions 1→N→G→Q→1 with N=C₂ and Q=C₂².₅₆C₂⁴

Direct product G=N×Q with N=C₂ and Q=C₂².₅₆C₂⁴

		d	ρ	Label	ID
C₂×C₂².₅₆C₂⁴		64		C2xC2^2.56C2^4	128,2259

Non-split extensions G=N.Q with N=C₂ and Q=C₂².₅₆C₂⁴

extension	φ:Q→Aut N	d	Label	ID
C₂.₁(C₂².₅₆C₂⁴) = C₂⁴.₂₂₅C₂³	central extension (φ=1)	64	C2.1(C2^2.56C2^4)	128,1108
C₂.₂(C₂².₅₆C₂⁴) = C₂³.₂₅₉C₂⁴	central extension (φ=1)	64	C2.2(C2^2.56C2^4)	128,1109
C₂.₃(C₂².₅₆C₂⁴) = C₂⁴.₂₂₇C₂³	central extension (φ=1)	64	C2.3(C2^2.56C2^4)	128,1110
C₂.₄(C₂².₅₆C₂⁴) = C₂³.₂₆₁C₂⁴	central extension (φ=1)	64	C2.4(C2^2.56C2^4)	128,1111
C₂.₅(C₂².₅₆C₂⁴) = C₂³.₂₆₄C₂⁴	central extension (φ=1)	128	C2.5(C2^2.56C2^4)	128,1114
C₂.₆(C₂².₅₆C₂⁴) = C₂³.₅₇₁C₂⁴	central stem extension (φ=1)	64	C2.6(C2^2.56C2^4)	128,1403
C₂.₇(C₂².₅₆C₂⁴) = C₂³.₅₇₂C₂⁴	central stem extension (φ=1)	64	C2.7(C2^2.56C2^4)	128,1404
C₂.₈(C₂².₅₆C₂⁴) = C₂³.₅₇₆C₂⁴	central stem extension (φ=1)	64	C2.8(C2^2.56C2^4)	128,1408
C₂.₉(C₂².₅₆C₂⁴) = C₂³.₅₈₁C₂⁴	central stem extension (φ=1)	64	C2.9(C2^2.56C2^4)	128,1413
C₂.₁₀(C₂².₅₆C₂⁴) = C₂⁴.₃₈₉C₂³	central stem extension (φ=1)	64	C2.10(C2^2.56C2^4)	128,1414
C₂.₁₁(C₂².₅₆C₂⁴) = C₂⁴.₃₉₃C₂³	central stem extension (φ=1)	64	C2.11(C2^2.56C2^4)	128,1418
C₂.₁₂(C₂².₅₆C₂⁴) = C₂⁴.₃₉₄C₂³	central stem extension (φ=1)	64	C2.12(C2^2.56C2^4)	128,1419
C₂.₁₃(C₂².₅₆C₂⁴) = C₂³.₅₉₂C₂⁴	central stem extension (φ=1)	64	C2.13(C2^2.56C2^4)	128,1424
C₂.₁₄(C₂².₅₆C₂⁴) = C₂⁴.₄₀₁C₂³	central stem extension (φ=1)	64	C2.14(C2^2.56C2^4)	128,1426
C₂.₁₅(C₂².₅₆C₂⁴) = C₂⁴.₄₀₃C₂³	central stem extension (φ=1)	64	C2.15(C2^2.56C2^4)	128,1428
C₂.₁₆(C₂².₅₆C₂⁴) = C₂³.₆₀₀C₂⁴	central stem extension (φ=1)	64	C2.16(C2^2.56C2^4)	128,1432
C₂.₁₇(C₂².₅₆C₂⁴) = C₂⁴.₄₀₇C₂³	central stem extension (φ=1)	64	C2.17(C2^2.56C2^4)	128,1433
C₂.₁₈(C₂².₅₆C₂⁴) = C₂⁴.₄₀₈C₂³	central stem extension (φ=1)	64	C2.18(C2^2.56C2^4)	128,1436
C₂.₁₉(C₂².₅₆C₂⁴) = C₂³.₆₀₆C₂⁴	central stem extension (φ=1)	64	C2.19(C2^2.56C2^4)	128,1438
C₂.₂₀(C₂².₅₆C₂⁴) = C₂³.₆₀₈C₂⁴	central stem extension (φ=1)	64	C2.20(C2^2.56C2^4)	128,1440
C₂.₂₁(C₂².₅₆C₂⁴) = C₂⁴.₄₁₂C₂³	central stem extension (φ=1)	64	C2.21(C2^2.56C2^4)	128,1442
C₂.₂₂(C₂².₅₆C₂⁴) = C₂³.₆₁₁C₂⁴	central stem extension (φ=1)	64	C2.22(C2^2.56C2^4)	128,1443
C₂.₂₃(C₂².₅₆C₂⁴) = C₂³.₆₃₀C₂⁴	central stem extension (φ=1)	64	C2.23(C2^2.56C2^4)	128,1462
C₂.₂₄(C₂².₅₆C₂⁴) = C₂³.₆₃₂C₂⁴	central stem extension (φ=1)	64	C2.24(C2^2.56C2^4)	128,1464
C₂.₂₅(C₂².₅₆C₂⁴) = C₂⁴.₄₂₇C₂³	central stem extension (φ=1)	64	C2.25(C2^2.56C2^4)	128,1471
C₂.₂₆(C₂².₅₆C₂⁴) = C₂³.₆₄₀C₂⁴	central stem extension (φ=1)	64	C2.26(C2^2.56C2^4)	128,1472
C₂.₂₇(C₂².₅₆C₂⁴) = C₂³.₆₄₁C₂⁴	central stem extension (φ=1)	64	C2.27(C2^2.56C2^4)	128,1473
C₂.₂₈(C₂².₅₆C₂⁴) = C₂³.₆₄₃C₂⁴	central stem extension (φ=1)	64	C2.28(C2^2.56C2^4)	128,1475
C₂.₂₉(C₂².₅₆C₂⁴) = C₂⁴.₄₃₀C₂³	central stem extension (φ=1)	64	C2.29(C2^2.56C2^4)	128,1476
C₂.₃₀(C₂².₅₆C₂⁴) = C₂³.₆₄₇C₂⁴	central stem extension (φ=1)	64	C2.30(C2^2.56C2^4)	128,1479
C₂.₃₁(C₂².₅₆C₂⁴) = C₂⁴.₄₃₅C₂³	central stem extension (φ=1)	64	C2.31(C2^2.56C2^4)	128,1482
C₂.₃₂(C₂².₅₆C₂⁴) = C₂³.₆₅₁C₂⁴	central stem extension (φ=1)	64	C2.32(C2^2.56C2^4)	128,1483
C₂.₃₃(C₂².₅₆C₂⁴) = C₂³.₆₅₄C₂⁴	central stem extension (φ=1)	64	C2.33(C2^2.56C2^4)	128,1486
C₂.₃₄(C₂².₅₆C₂⁴) = C₂³.₆₅₅C₂⁴	central stem extension (φ=1)	128	C2.34(C2^2.56C2^4)	128,1487
C₂.₃₅(C₂².₅₆C₂⁴) = C₂⁴.₄₄₀C₂³	central stem extension (φ=1)	64	C2.35(C2^2.56C2^4)	128,1493
C₂.₃₆(C₂².₅₆C₂⁴) = C₂³.₆₆₈C₂⁴	central stem extension (φ=1)	64	C2.36(C2^2.56C2^4)	128,1500
C₂.₃₇(C₂².₅₆C₂⁴) = C₂³.₆₇₂C₂⁴	central stem extension (φ=1)	64	C2.37(C2^2.56C2^4)	128,1504
C₂.₃₈(C₂².₅₆C₂⁴) = C₂³.₆₇₉C₂⁴	central stem extension (φ=1)	64	C2.38(C2^2.56C2^4)	128,1511
C₂.₃₉(C₂².₅₆C₂⁴) = C₂³.₆₈₁C₂⁴	central stem extension (φ=1)	64	C2.39(C2^2.56C2^4)	128,1513
C₂.₄₀(C₂².₅₆C₂⁴) = C₂³.₆₈₃C₂⁴	central stem extension (φ=1)	64	C2.40(C2^2.56C2^4)	128,1515
C₂.₄₁(C₂².₅₆C₂⁴) = C₂³.₆₈₆C₂⁴	central stem extension (φ=1)	64	C2.41(C2^2.56C2^4)	128,1518
C₂.₄₂(C₂².₅₆C₂⁴) = C₂³.₆₈₈C₂⁴	central stem extension (φ=1)	64	C2.42(C2^2.56C2^4)	128,1520
C₂.₄₃(C₂².₅₆C₂⁴) = C₂³.₆₉₈C₂⁴	central stem extension (φ=1)	64	C2.43(C2^2.56C2^4)	128,1530
C₂.₄₄(C₂².₅₆C₂⁴) = C₂³.₇₀₀C₂⁴	central stem extension (φ=1)	64	C2.44(C2^2.56C2^4)	128,1532
C₂.₄₅(C₂².₅₆C₂⁴) = C₂³.₇₀₂C₂⁴	central stem extension (φ=1)	128	C2.45(C2^2.56C2^4)	128,1534
C₂.₄₆(C₂².₅₆C₂⁴) = C₂³.₇₀₆C₂⁴	central stem extension (φ=1)	128	C2.46(C2^2.56C2^4)	128,1538
C₂.₄₇(C₂².₅₆C₂⁴) = C₂³.₇₀₈C₂⁴	central stem extension (φ=1)	64	C2.47(C2^2.56C2^4)	128,1540
C₂.₄₈(C₂².₅₆C₂⁴) = C₂⁴.₄₅₉C₂³	central stem extension (φ=1)	64	C2.48(C2^2.56C2^4)	128,1545
C₂.₄₉(C₂².₅₆C₂⁴) = C₂³.₇₁₄C₂⁴	central stem extension (φ=1)	64	C2.49(C2^2.56C2^4)	128,1546
C₂.₅₀(C₂².₅₆C₂⁴) = C₂³.₇₁₆C₂⁴	central stem extension (φ=1)	64	C2.50(C2^2.56C2^4)	128,1548
C₂.₅₁(C₂².₅₆C₂⁴) = C₄²⋊₃₄D₄	central stem extension (φ=1)	64	C2.51(C2^2.56C2^4)	128,1551
C₂.₅₂(C₂².₅₆C₂⁴) = C₄².₁₉₉D₄	central stem extension (φ=1)	64	C2.52(C2^2.56C2^4)	128,1552
C₂.₅₃(C₂².₅₆C₂⁴) = C₂³.₇₂₄C₂⁴	central stem extension (φ=1)	64	C2.53(C2^2.56C2^4)	128,1556
C₂.₅₄(C₂².₅₆C₂⁴) = C₂³.₇₂₆C₂⁴	central stem extension (φ=1)	64	C2.54(C2^2.56C2^4)	128,1558
C₂.₅₅(C₂².₅₆C₂⁴) = C₂³.₇₂₇C₂⁴	central stem extension (φ=1)	64	C2.55(C2^2.56C2^4)	128,1559
C₂.₅₆(C₂².₅₆C₂⁴) = C₂³.₇₂₉C₂⁴	central stem extension (φ=1)	64	C2.56(C2^2.56C2^4)	128,1561
C₂.₅₇(C₂².₅₆C₂⁴) = C₂³.₇₃₀C₂⁴	central stem extension (φ=1)	64	C2.57(C2^2.56C2^4)	128,1562
C₂.₅₈(C₂².₅₆C₂⁴) = C₂³.₇₃₁C₂⁴	central stem extension (φ=1)	64	C2.58(C2^2.56C2^4)	128,1563
C₂.₅₉(C₂².₅₆C₂⁴) = C₂³.₇₃₂C₂⁴	central stem extension (φ=1)	64	C2.59(C2^2.56C2^4)	128,1564
C₂.₆₀(C₂².₅₆C₂⁴) = C₂³.₇₃₆C₂⁴	central stem extension (φ=1)	64	C2.60(C2^2.56C2^4)	128,1568
C₂.₆₁(C₂².₅₆C₂⁴) = C₂³.₇₃₇C₂⁴	central stem extension (φ=1)	64	C2.61(C2^2.56C2^4)	128,1569
C₂.₆₂(C₂².₅₆C₂⁴) = C₂³.₇₃₉C₂⁴	central stem extension (φ=1)	128	C2.62(C2^2.56C2^4)	128,1571
C₂.₆₃(C₂².₅₆C₂⁴) = C₂³.₇₄₁C₂⁴	central stem extension (φ=1)	64	C2.63(C2^2.56C2^4)	128,1573
C₂.₆₄(C₂².₅₆C₂⁴) = C₄².₄₀Q₈	central stem extension (φ=1)	128	C2.64(C2^2.56C2^4)	128,1577

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Extensions 1→N→G→Q→1 with N=C2 and Q=C22.56C24

Extensions 1→N→G→Q→1 with N=C₂ and Q=C₂².₅₆C₂⁴