Extensions 1→N→G→Q→1 with N=C₂ and Q=C₂².₅₄C₂⁴

Direct product G=N×Q with N=C₂ and Q=C₂².₅₄C₂⁴

		d	ρ	Label	ID
C₂×C₂².₅₄C₂⁴		32		C2xC2^2.54C2^4	128,2257

Non-split extensions G=N.Q with N=C₂ and Q=C₂².₅₄C₂⁴

extension	φ:Q→Aut N	d	Label	ID
C₂.₁(C₂².₅₄C₂⁴) = C₂³.₂₅₇C₂⁴	central extension (φ=1)	32	C2.1(C2^2.54C2^4)	128,1107
C₂.₂(C₂².₅₄C₂⁴) = C₂⁴.₂₂₅C₂³	central extension (φ=1)	64	C2.2(C2^2.54C2^4)	128,1108
C₂.₃(C₂².₅₄C₂⁴) = C₂³.₂₅₉C₂⁴	central extension (φ=1)	64	C2.3(C2^2.54C2^4)	128,1109
C₂.₄(C₂².₅₄C₂⁴) = C₂³.₂₆₂C₂⁴	central extension (φ=1)	64	C2.4(C2^2.54C2^4)	128,1112
C₂.₅(C₂².₅₄C₂⁴) = C₂⁴.₂₃₀C₂³	central extension (φ=1)	64	C2.5(C2^2.54C2^4)	128,1115
C₂.₆(C₂².₅₄C₂⁴) = C₂³.₅₆₈C₂⁴	central stem extension (φ=1)	32	C2.6(C2^2.54C2^4)	128,1400
C₂.₇(C₂².₅₄C₂⁴) = C₂³.₅₆₉C₂⁴	central stem extension (φ=1)	32	C2.7(C2^2.54C2^4)	128,1401
C₂.₈(C₂².₅₄C₂⁴) = C₂³.₅₇₃C₂⁴	central stem extension (φ=1)	64	C2.8(C2^2.54C2^4)	128,1405
C₂.₉(C₂².₅₄C₂⁴) = C₂⁴.₃₈₄C₂³	central stem extension (φ=1)	64	C2.9(C2^2.54C2^4)	128,1407
C₂.₁₀(C₂².₅₄C₂⁴) = C₂³.₅₇₈C₂⁴	central stem extension (φ=1)	32	C2.10(C2^2.54C2^4)	128,1410
C₂.₁₁(C₂².₅₄C₂⁴) = C₂³.₅₈₅C₂⁴	central stem extension (φ=1)	32	C2.11(C2^2.54C2^4)	128,1417
C₂.₁₂(C₂².₅₄C₂⁴) = C₂⁴.₃₉₅C₂³	central stem extension (φ=1)	64	C2.12(C2^2.54C2^4)	128,1420
C₂.₁₃(C₂².₅₄C₂⁴) = C₂³.₅₉₁C₂⁴	central stem extension (φ=1)	64	C2.13(C2^2.54C2^4)	128,1423
C₂.₁₄(C₂².₅₄C₂⁴) = C₂³.₅₉₃C₂⁴	central stem extension (φ=1)	64	C2.14(C2^2.54C2^4)	128,1425
C₂.₁₅(C₂².₅₄C₂⁴) = C₂³.₅₉₇C₂⁴	central stem extension (φ=1)	32	C2.15(C2^2.54C2^4)	128,1429
C₂.₁₆(C₂².₅₄C₂⁴) = C₂⁴.₄₀₆C₂³	central stem extension (φ=1)	64	C2.16(C2^2.54C2^4)	128,1431
C₂.₁₇(C₂².₅₄C₂⁴) = C₂³.₆₀₃C₂⁴	central stem extension (φ=1)	64	C2.17(C2^2.54C2^4)	128,1435
C₂.₁₈(C₂².₅₄C₂⁴) = C₂³.₆₀₅C₂⁴	central stem extension (φ=1)	64	C2.18(C2^2.54C2^4)	128,1437
C₂.₁₉(C₂².₅₄C₂⁴) = C₂⁴.₄₁₁C₂³	central stem extension (φ=1)	64	C2.19(C2^2.54C2^4)	128,1441
C₂.₂₀(C₂².₅₄C₂⁴) = C₂⁴.₄₁₃C₂³	central stem extension (φ=1)	64	C2.20(C2^2.54C2^4)	128,1446
C₂.₂₁(C₂².₅₄C₂⁴) = C₂³.₆₃₅C₂⁴	central stem extension (φ=1)	32	C2.21(C2^2.54C2^4)	128,1467
C₂.₂₂(C₂².₅₄C₂⁴) = C₂³.₆₃₇C₂⁴	central stem extension (φ=1)	64	C2.22(C2^2.54C2^4)	128,1469
C₂.₂₃(C₂².₅₄C₂⁴) = C₂⁴.₄₂₈C₂³	central stem extension (φ=1)	64	C2.23(C2^2.54C2^4)	128,1474
C₂.₂₄(C₂².₅₄C₂⁴) = C₂⁴.₄₃₂C₂³	central stem extension (φ=1)	64	C2.24(C2^2.54C2^4)	128,1478
C₂.₂₅(C₂².₅₄C₂⁴) = C₂⁴.₄₃₄C₂³	central stem extension (φ=1)	64	C2.25(C2^2.54C2^4)	128,1480
C₂.₂₆(C₂².₅₄C₂⁴) = C₂³.₆₄₉C₂⁴	central stem extension (φ=1)	64	C2.26(C2^2.54C2^4)	128,1481
C₂.₂₇(C₂².₅₄C₂⁴) = C₂³.₆₅₂C₂⁴	central stem extension (φ=1)	64	C2.27(C2^2.54C2^4)	128,1484
C₂.₂₈(C₂².₅₄C₂⁴) = C₂³.₆₅₆C₂⁴	central stem extension (φ=1)	64	C2.28(C2^2.54C2^4)	128,1488
C₂.₂₉(C₂².₅₄C₂⁴) = C₂⁴.₄₃₈C₂³	central stem extension (φ=1)	64	C2.29(C2^2.54C2^4)	128,1489
C₂.₃₀(C₂².₅₄C₂⁴) = C₂³.₆₆₀C₂⁴	central stem extension (φ=1)	64	C2.30(C2^2.54C2^4)	128,1492
C₂.₃₁(C₂².₅₄C₂⁴) = C₂³.₆₇₈C₂⁴	central stem extension (φ=1)	64	C2.31(C2^2.54C2^4)	128,1510
C₂.₃₂(C₂².₅₄C₂⁴) = C₂⁴.₄₄₈C₂³	central stem extension (φ=1)	64	C2.32(C2^2.54C2^4)	128,1512
C₂.₃₃(C₂².₅₄C₂⁴) = C₂⁴.₄₅₀C₂³	central stem extension (φ=1)	64	C2.33(C2^2.54C2^4)	128,1516
C₂.₃₄(C₂².₅₄C₂⁴) = C₂⁴.₄₅₄C₂³	central stem extension (φ=1)	64	C2.34(C2^2.54C2^4)	128,1522
C₂.₃₅(C₂².₅₄C₂⁴) = C₂³.₆₉₂C₂⁴	central stem extension (φ=1)	128	C2.35(C2^2.54C2^4)	128,1524
C₂.₃₆(C₂².₅₄C₂⁴) = C₂³.₆₉₅C₂⁴	central stem extension (φ=1)	64	C2.36(C2^2.54C2^4)	128,1527
C₂.₃₇(C₂².₅₄C₂⁴) = C₂³.₆₉₆C₂⁴	central stem extension (φ=1)	64	C2.37(C2^2.54C2^4)	128,1528
C₂.₃₈(C₂².₅₄C₂⁴) = C₂³.₆₉₇C₂⁴	central stem extension (φ=1)	64	C2.38(C2^2.54C2^4)	128,1529
C₂.₃₉(C₂².₅₄C₂⁴) = C₂³.₇₀₁C₂⁴	central stem extension (φ=1)	64	C2.39(C2^2.54C2^4)	128,1533
C₂.₄₀(C₂².₅₄C₂⁴) = C₂³.₇₀₃C₂⁴	central stem extension (φ=1)	64	C2.40(C2^2.54C2^4)	128,1535
C₂.₄₁(C₂².₅₄C₂⁴) = C₂³.₇₀₇C₂⁴	central stem extension (φ=1)	64	C2.41(C2^2.54C2^4)	128,1539
C₂.₄₂(C₂².₅₄C₂⁴) = C₂⁴⋊₁₁D₄	central stem extension (φ=1)	32	C2.42(C2^2.54C2^4)	128,1544
C₂.₄₃(C₂².₅₄C₂⁴) = C₂⁴.₄₅₉C₂³	central stem extension (φ=1)	64	C2.43(C2^2.54C2^4)	128,1545
C₂.₄₄(C₂².₅₄C₂⁴) = C₂³.₇₁₅C₂⁴	central stem extension (φ=1)	64	C2.44(C2^2.54C2^4)	128,1547
C₂.₄₅(C₂².₅₄C₂⁴) = C₄²⋊₃₃D₄	central stem extension (φ=1)	64	C2.45(C2^2.54C2^4)	128,1550
C₂.₄₆(C₂².₅₄C₂⁴) = C₄²⋊₃₅D₄	central stem extension (φ=1)	64	C2.46(C2^2.54C2^4)	128,1555
C₂.₄₇(C₂².₅₄C₂⁴) = C₂³.₇₂₄C₂⁴	central stem extension (φ=1)	64	C2.47(C2^2.54C2^4)	128,1556
C₂.₄₈(C₂².₅₄C₂⁴) = C₂³.₇₂₅C₂⁴	central stem extension (φ=1)	64	C2.48(C2^2.54C2^4)	128,1557
C₂.₄₉(C₂².₅₄C₂⁴) = C₂³.₇₂₆C₂⁴	central stem extension (φ=1)	64	C2.49(C2^2.54C2^4)	128,1558
C₂.₅₀(C₂².₅₄C₂⁴) = C₂³.₇₂₇C₂⁴	central stem extension (φ=1)	64	C2.50(C2^2.54C2^4)	128,1559
C₂.₅₁(C₂².₅₄C₂⁴) = C₂³.₇₂₈C₂⁴	central stem extension (φ=1)	64	C2.51(C2^2.54C2^4)	128,1560
C₂.₅₂(C₂².₅₄C₂⁴) = C₂³.₇₂₉C₂⁴	central stem extension (φ=1)	64	C2.52(C2^2.54C2^4)	128,1561
C₂.₅₃(C₂².₅₄C₂⁴) = C₂³.₇₃₀C₂⁴	central stem extension (φ=1)	64	C2.53(C2^2.54C2^4)	128,1562
C₂.₅₄(C₂².₅₄C₂⁴) = C₂³.₇₃₄C₂⁴	central stem extension (φ=1)	64	C2.54(C2^2.54C2^4)	128,1566
C₂.₅₅(C₂².₅₄C₂⁴) = C₂³.₇₃₇C₂⁴	central stem extension (φ=1)	64	C2.55(C2^2.54C2^4)	128,1569
C₂.₅₆(C₂².₅₄C₂⁴) = C₂³.₇₃₈C₂⁴	central stem extension (φ=1)	64	C2.56(C2^2.54C2^4)	128,1570
C₂.₅₇(C₂².₅₄C₂⁴) = C₂³.₇₄₁C₂⁴	central stem extension (φ=1)	64	C2.57(C2^2.54C2^4)	128,1573
C₂.₅₈(C₂².₅₄C₂⁴) = C₂⁴.₁₅Q₈	central stem extension (φ=1)	32	C2.58(C2^2.54C2^4)	128,1574
C₂.₅₉(C₂².₅₄C₂⁴) = C₄²⋊₁₂Q₈	central stem extension (φ=1)	128	C2.59(C2^2.54C2^4)	128,1575

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Extensions 1→N→G→Q→1 with N=C2 and Q=C22.54C24

Extensions 1→N→G→Q→1 with N=C₂ and Q=C₂².₅₄C₂⁴