Extensions 1→N→G→Q→1 with N=C₅₂ and Q=D₄

Direct product G=N×Q with N=C₅₂ and Q=D₄

		d	ρ	Label	ID
D₄×C₅₂		208		D4xC52	416,179

Semidirect products G=N:Q with N=C₅₂ and Q=D₄

extension	φ:Q→Aut N	d	Label	ID
C₅₂⋊₁D₄ = C₄⋊₂D₅₂	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	C52:1D4	416,116
C₅₂⋊₂D₄ = C₅₂⋊₂D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	C52:2D4	416,159
C₅₂⋊₃D₄ = C₅₂⋊D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	C52:3D4	416,161
C₅₂⋊₄D₄ = C₄⋊D₅₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	C52:4D4	416,95
C₅₂⋊₅D₄ = C₄×D₅₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	C52:5D4	416,94
C₅₂⋊₆D₄ = C₁₃×C₄⋊₁D₄	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	C52:6D4	416,188
C₅₂⋊₇D₄ = C₅₂⋊₇D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	C52:7D4	416,151
C₅₂⋊₈D₄ = C₄×C₁₃⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	C52:8D4	416,149
C₅₂⋊₉D₄ = C₁₃×C₄⋊D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	C52:9D4	416,182

Non-split extensions G=N.Q with N=C₅₂ and Q=D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₂.₁D₄ = D₅₂⋊₆C₄	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.1D4	416,16
C₅₂.₂D₄ = C₂₆.Q₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	416		C52.2D4	416,17
C₅₂.₃D₄ = C₁₃⋊D₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	4+	C52.3D4	416,33
C₅₂.₄D₄ = D₈.D₁₃	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	4-	C52.4D4	416,34
C₅₂.₅D₄ = C₈.₆D₂₆	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	4+	C52.5D4	416,35
C₅₂.₆D₄ = C₁₃⋊Q₃₂	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	416	4-	C52.6D4	416,36
C₅₂.₇D₄ = D₄⋊Dic₁₃	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.7D4	416,39
C₅₂.₈D₄ = C₅₂.D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	104	4	C52.8D4	416,40
C₅₂.₉D₄ = Q₈⋊Dic₁₃	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	416		C52.9D4	416,42
C₅₂.₁₀D₄ = C₅₂.₁₀D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	4	C52.10D4	416,43
C₅₂.₁₁D₄ = D₂₆⋊₂Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.11D4	416,118
C₅₂.₁₂D₄ = C₈⋊D₂₆	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	104	4+	C52.12D4	416,129
C₅₂.₁₃D₄ = C₈.D₂₆	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	4-	C52.13D4	416,130
C₅₂.₁₄D₄ = C₂×D₄⋊D₁₃	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.14D4	416,152
C₅₂.₁₅D₄ = D₅₂⋊₆C₂²	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	104	4	C52.15D4	416,153
C₅₂.₁₆D₄ = C₂×D₄.D₁₃	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.16D4	416,154
C₅₂.₁₇D₄ = C₅₂.₁₇D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.17D4	416,157
C₅₂.₁₈D₄ = C₂×Q₈⋊D₁₃	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.18D4	416,162
C₅₂.₁₉D₄ = Q₈.D₂₆	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208	4	C52.19D4	416,163
C₅₂.₂₀D₄ = C₂×C₁₃⋊Q₁₆	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	416		C52.20D4	416,164
C₅₂.₂₁D₄ = Dic₁₃⋊Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	416		C52.21D4	416,165
C₅₂.₂₂D₄ = D₂₆⋊₃Q₈	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.22D4	416,167
C₅₂.₂₃D₄ = C₅₂.₂₃D₄	φ: D₄/C₂ → C₂² ⊆ Aut C₅₂	208		C52.23D4	416,168
C₅₂.₂₄D₄ = D₂₀₈	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	2+	C52.24D4	416,6
C₅₂.₂₅D₄ = C₁₆⋊D₁₃	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	2	C52.25D4	416,7
C₅₂.₂₆D₄ = Dic₁₀₄	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	416	2-	C52.26D4	416,8
C₅₂.₂₇D₄ = C₅₂⋊₂Q₈	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	416		C52.27D4	416,90
C₅₂.₂₈D₄ = C₄.D₅₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208		C52.28D4	416,96
C₅₂.₂₉D₄ = C₂×C₁₀₄⋊C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208		C52.29D4	416,123
C₅₂.₃₀D₄ = C₂×D₁₀₄	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208		C52.30D4	416,124
C₅₂.₃₁D₄ = C₂×Dic₅₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	416		C52.31D4	416,126
C₅₂.₃₂D₄ = C₅₂⋊₃C₈	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	416		C52.32D4	416,11
C₅₂.₃₃D₄ = D₅₂⋊₄C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	104	2	C52.33D4	416,12
C₅₂.₃₄D₄ = C₁₀₄.₆C₄	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	2	C52.34D4	416,26
C₅₂.₃₅D₄ = D₁₀₄⋊₇C₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	2	C52.35D4	416,125
C₅₂.₃₆D₄ = C₁₃×D₁₆	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	2	C52.36D4	416,61
C₅₂.₃₇D₄ = C₁₃×SD₃₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208	2	C52.37D4	416,62
C₅₂.₃₈D₄ = C₁₃×Q₃₂	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	416	2	C52.38D4	416,63
C₅₂.₃₉D₄ = C₁₃×C₄.₄D₄	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208		C52.39D4	416,185
C₅₂.₄₀D₄ = C₁₃×C₄⋊Q₈	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	416		C52.40D4	416,189
C₅₂.₄₁D₄ = D₈×C₂₆	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208		C52.41D4	416,193
C₅₂.₄₂D₄ = SD₁₆×C₂₆	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	208		C52.42D4	416,194
C₅₂.₄₃D₄ = Q₁₆×C₂₆	φ: D₄/C₄ → C₂ ⊆ Aut C₅₂	416		C52.43D4	416,195
C₅₂.₄₄D₄ = C₅₂.₄₄D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	416		C52.44D4	416,23
C₅₂.₄₅D₄ = D₅₂⋊₅C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208		C52.45D4	416,28
C₅₂.₄₆D₄ = C₅₂.₄₆D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	104	4+	C52.46D4	416,30
C₅₂.₄₇D₄ = C₄.₁₂D₅₂	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	4-	C52.47D4	416,31
C₅₂.₄₈D₄ = C₅₂.₄₈D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208		C52.48D4	416,145
C₅₂.₄₉D₄ = D₄⋊D₂₆	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	104	4+	C52.49D4	416,170
C₅₂.₅₀D₄ = D₄.₉D₂₆	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	4-	C52.50D4	416,172
C₅₂.₅₁D₄ = C₅₂.₈Q₈	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	416		C52.51D4	416,21
C₅₂.₅₂D₄ = D₂₆⋊₁C₈	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208		C52.52D4	416,27
C₅₂.₅₃D₄ = C₅₂.₅₃D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	4	C52.53D4	416,29
C₅₂.₅₄D₄ = D₅₂⋊₇C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	104	4	C52.54D4	416,32
C₅₂.₅₅D₄ = C₅₂.₅₅D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208		C52.55D4	416,37
C₅₂.₅₆D₄ = C₅₂.₅₆D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	104	4	C52.56D4	416,44
C₅₂.₅₇D₄ = C₅₂.C₂³	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	4	C52.57D4	416,171
C₅₂.₅₈D₄ = C₁₃×C₄.D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	104	4	C52.58D4	416,50
C₅₂.₅₉D₄ = C₁₃×C₄.₁₀D₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	4	C52.59D4	416,51
C₅₂.₆₀D₄ = C₁₃×D₄⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208		C52.60D4	416,52
C₅₂.₆₁D₄ = C₁₃×Q₈⋊C₄	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	416		C52.61D4	416,53
C₅₂.₆₂D₄ = C₁₃×C₂²⋊Q₈	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208		C52.62D4	416,183
C₅₂.₆₃D₄ = C₁₃×C₈⋊C₂²	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	104	4	C52.63D4	416,197
C₅₂.₆₄D₄ = C₁₃×C₈.C₂²	φ: D₄/C₂² → C₂ ⊆ Aut C₅₂	208	4	C52.64D4	416,198
C₅₂.₆₅D₄ = C₁₃×C₂²⋊C₈	central extension (φ=1)	208		C52.65D4	416,48
C₅₂.₆₆D₄ = C₁₃×C₄≀C₂	central extension (φ=1)	104	2	C52.66D4	416,54
C₅₂.₆₇D₄ = C₁₃×C₄⋊C₈	central extension (φ=1)	416		C52.67D4	416,55
C₅₂.₆₈D₄ = C₁₃×C₈.C₄	central extension (φ=1)	208	2	C52.68D4	416,58
C₅₂.₆₉D₄ = C₁₃×C₄○D₈	central extension (φ=1)	208	2	C52.69D4	416,196

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Extensions 1→N→G→Q→1 with N=C52 and Q=D4

Extensions 1→N→G→Q→1 with N=C₅₂ and Q=D₄