Extensions 1→N→G→Q→1 with N=C4 and Q=2- 1+4

Direct product G=N×Q with N=C4 and Q=2- 1+4
dρLabelID
C4×2- 1+464C4xES-(2,2)128,2162

Semidirect products G=N:Q with N=C4 and Q=2- 1+4
extensionφ:Q→Aut NdρLabelID
C412- 1+4 = C4⋊2- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4:1ES-(2,2)128,2229
C422- 1+4 = C22.88C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4:2ES-(2,2)128,2231

Non-split extensions G=N.Q with N=C4 and Q=2- 1+4
extensionφ:Q→Aut NdρLabelID
C4.12- 1+4 = C42.293D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.1ES-(2,2)128,1977
C4.22- 1+4 = C42.294D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.2ES-(2,2)128,1978
C4.32- 1+4 = C42.295D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.3ES-(2,2)128,1979
C4.42- 1+4 = C42.296D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.4ES-(2,2)128,1980
C4.52- 1+4 = C42.297D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.5ES-(2,2)128,1981
C4.62- 1+4 = C42.298D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.6ES-(2,2)128,1982
C4.72- 1+4 = C42.299D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.7ES-(2,2)128,1983
C4.82- 1+4 = C42.300D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.8ES-(2,2)128,1984
C4.92- 1+4 = C42.301D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.9ES-(2,2)128,1985
C4.102- 1+4 = C42.302D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.10ES-(2,2)128,1986
C4.112- 1+4 = C42.303D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.11ES-(2,2)128,1987
C4.122- 1+4 = C42.304D4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.12ES-(2,2)128,1988
C4.132- 1+4 = C4.2- 1+4φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.13ES-(2,2)128,1989
C4.142- 1+4 = C42.25C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.14ES-(2,2)128,1990
C4.152- 1+4 = C42.26C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.15ES-(2,2)128,1991
C4.162- 1+4 = C42.27C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.16ES-(2,2)128,1992
C4.172- 1+4 = C42.28C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.17ES-(2,2)128,1993
C4.182- 1+4 = C42.29C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.18ES-(2,2)128,1994
C4.192- 1+4 = C42.30C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.19ES-(2,2)128,1995
C4.202- 1+4 = Q84D8φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.20ES-(2,2)128,2090
C4.212- 1+4 = Q87SD16φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.21ES-(2,2)128,2091
C4.222- 1+4 = C42.501C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.22ES-(2,2)128,2092
C4.232- 1+4 = C42.502C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.23ES-(2,2)128,2093
C4.242- 1+4 = Q88SD16φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.24ES-(2,2)128,2094
C4.252- 1+4 = Q85Q16φ: 2- 1+4/C2×Q8C2 ⊆ Aut C4128C4.25ES-(2,2)128,2095
C4.262- 1+4 = C42.505C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.26ES-(2,2)128,2096
C4.272- 1+4 = C42.506C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.27ES-(2,2)128,2097
C4.282- 1+4 = C42.507C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.28ES-(2,2)128,2098
C4.292- 1+4 = C42.508C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.29ES-(2,2)128,2099
C4.302- 1+4 = C42.509C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.30ES-(2,2)128,2100
C4.312- 1+4 = C42.510C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.31ES-(2,2)128,2101
C4.322- 1+4 = C42.511C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.32ES-(2,2)128,2102
C4.332- 1+4 = C42.512C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.33ES-(2,2)128,2103
C4.342- 1+4 = C42.513C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.34ES-(2,2)128,2104
C4.352- 1+4 = C42.514C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.35ES-(2,2)128,2105
C4.362- 1+4 = C42.515C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C4128C4.36ES-(2,2)128,2106
C4.372- 1+4 = C42.516C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.37ES-(2,2)128,2107
C4.382- 1+4 = C42.517C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.38ES-(2,2)128,2108
C4.392- 1+4 = C42.518C23φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.39ES-(2,2)128,2109
C4.402- 1+4 = C22.91C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.40ES-(2,2)128,2234
C4.412- 1+4 = C22.96C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.41ES-(2,2)128,2239
C4.422- 1+4 = C22.111C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.42ES-(2,2)128,2254
C4.432- 1+4 = C23.146C24φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.43ES-(2,2)128,2255
C4.442- 1+4 = C22.137C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.44ES-(2,2)128,2280
C4.452- 1+4 = C22.139C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.45ES-(2,2)128,2282
C4.462- 1+4 = C22.143C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.46ES-(2,2)128,2286
C4.472- 1+4 = C22.144C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.47ES-(2,2)128,2287
C4.482- 1+4 = C22.145C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.48ES-(2,2)128,2288
C4.492- 1+4 = C22.146C25φ: 2- 1+4/C2×Q8C2 ⊆ Aut C464C4.49ES-(2,2)128,2289
C4.502- 1+4 = C42.278D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.50ES-(2,2)128,1958
C4.512- 1+4 = C42.279D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.51ES-(2,2)128,1959
C4.522- 1+4 = C42.280D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.52ES-(2,2)128,1960
C4.532- 1+4 = C42.281D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.53ES-(2,2)128,1961
C4.542- 1+4 = C42.282D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.54ES-(2,2)128,1962
C4.552- 1+4 = C42.283D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.55ES-(2,2)128,1963
C4.562- 1+4 = C42.284D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.56ES-(2,2)128,1964
C4.572- 1+4 = C42.285D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.57ES-(2,2)128,1965
C4.582- 1+4 = C42.286D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.58ES-(2,2)128,1966
C4.592- 1+4 = C42.287D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.59ES-(2,2)128,1967
C4.602- 1+4 = C42.288D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.60ES-(2,2)128,1968
C4.612- 1+4 = C42.289D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.61ES-(2,2)128,1969
C4.622- 1+4 = C42.290D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.62ES-(2,2)128,1970
C4.632- 1+4 = C42.291D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.63ES-(2,2)128,1971
C4.642- 1+4 = C42.292D4φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.64ES-(2,2)128,1972
C4.652- 1+4 = C42.423C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.65ES-(2,2)128,1973
C4.662- 1+4 = C42.424C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.66ES-(2,2)128,1974
C4.672- 1+4 = C42.425C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.67ES-(2,2)128,1975
C4.682- 1+4 = C42.426C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.68ES-(2,2)128,1976
C4.692- 1+4 = D45D8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.69ES-(2,2)128,2066
C4.702- 1+4 = D49SD16φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.70ES-(2,2)128,2067
C4.712- 1+4 = C42.485C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.71ES-(2,2)128,2068
C4.722- 1+4 = C42.486C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.72ES-(2,2)128,2069
C4.732- 1+4 = D46Q16φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.73ES-(2,2)128,2070
C4.742- 1+4 = C42.488C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.74ES-(2,2)128,2071
C4.752- 1+4 = C42.489C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.75ES-(2,2)128,2072
C4.762- 1+4 = C42.490C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.76ES-(2,2)128,2073
C4.772- 1+4 = C42.491C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.77ES-(2,2)128,2074
C4.782- 1+4 = C42.57C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.78ES-(2,2)128,2075
C4.792- 1+4 = C42.58C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.79ES-(2,2)128,2076
C4.802- 1+4 = C42.59C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.80ES-(2,2)128,2077
C4.812- 1+4 = C42.60C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.81ES-(2,2)128,2078
C4.822- 1+4 = C42.61C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.82ES-(2,2)128,2079
C4.832- 1+4 = C42.62C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.83ES-(2,2)128,2080
C4.842- 1+4 = C42.63C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.84ES-(2,2)128,2081
C4.852- 1+4 = C42.64C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.85ES-(2,2)128,2082
C4.862- 1+4 = C42.492C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.86ES-(2,2)128,2083
C4.872- 1+4 = C42.493C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.87ES-(2,2)128,2084
C4.882- 1+4 = C42.494C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.88ES-(2,2)128,2085
C4.892- 1+4 = C42.495C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.89ES-(2,2)128,2086
C4.902- 1+4 = C42.496C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.90ES-(2,2)128,2087
C4.912- 1+4 = C42.497C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.91ES-(2,2)128,2088
C4.922- 1+4 = C42.498C23φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.92ES-(2,2)128,2089
C4.932- 1+4 = Q8×D8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.93ES-(2,2)128,2110
C4.942- 1+4 = Q8×SD16φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.94ES-(2,2)128,2111
C4.952- 1+4 = D86Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.95ES-(2,2)128,2112
C4.962- 1+4 = SD164Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.96ES-(2,2)128,2113
C4.972- 1+4 = Q8×Q16φ: 2- 1+4/C4○D4C2 ⊆ Aut C4128C4.97ES-(2,2)128,2114
C4.982- 1+4 = Q166Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C4128C4.98ES-(2,2)128,2115
C4.992- 1+4 = D84Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.99ES-(2,2)128,2116
C4.1002- 1+4 = SD16⋊Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.100ES-(2,2)128,2117
C4.1012- 1+4 = SD162Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.101ES-(2,2)128,2118
C4.1022- 1+4 = Q164Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C4128C4.102ES-(2,2)128,2119
C4.1032- 1+4 = SD163Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.103ES-(2,2)128,2120
C4.1042- 1+4 = D85Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.104ES-(2,2)128,2121
C4.1052- 1+4 = Q165Q8φ: 2- 1+4/C4○D4C2 ⊆ Aut C4128C4.105ES-(2,2)128,2122
C4.1062- 1+4 = C22.92C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.106ES-(2,2)128,2235
C4.1072- 1+4 = C22.98C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.107ES-(2,2)128,2241
C4.1082- 1+4 = C22.100C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.108ES-(2,2)128,2243
C4.1092- 1+4 = C22.104C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.109ES-(2,2)128,2247
C4.1102- 1+4 = C22.107C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.110ES-(2,2)128,2250
C4.1112- 1+4 = C22.133C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.111ES-(2,2)128,2276
C4.1122- 1+4 = C22.136C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.112ES-(2,2)128,2279
C4.1132- 1+4 = C22.141C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.113ES-(2,2)128,2284
C4.1142- 1+4 = C22.148C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.114ES-(2,2)128,2291
C4.1152- 1+4 = C22.152C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.115ES-(2,2)128,2295
C4.1162- 1+4 = C22.154C25φ: 2- 1+4/C4○D4C2 ⊆ Aut C464C4.116ES-(2,2)128,2297
C4.1172- 1+4 = C42.695C23central extension (φ=1)64C4.117ES-(2,2)128,1714
C4.1182- 1+4 = C42.302C23central extension (φ=1)64C4.118ES-(2,2)128,1715
C4.1192- 1+4 = Q8.4M4(2)central extension (φ=1)64C4.119ES-(2,2)128,1716
C4.1202- 1+4 = C42.696C23central extension (φ=1)64C4.120ES-(2,2)128,1717
C4.1212- 1+4 = C42.304C23central extension (φ=1)64C4.121ES-(2,2)128,1718
C4.1222- 1+4 = C42.305C23central extension (φ=1)64C4.122ES-(2,2)128,1719
C4.1232- 1+4 = C42.697C23central extension (φ=1)64C4.123ES-(2,2)128,1720
C4.1242- 1+4 = C42.698C23central extension (φ=1)64C4.124ES-(2,2)128,1721
C4.1252- 1+4 = D48M4(2)central extension (φ=1)64C4.125ES-(2,2)128,1722
C4.1262- 1+4 = Q87M4(2)central extension (φ=1)64C4.126ES-(2,2)128,1723
C4.1272- 1+4 = C42.307C23central extension (φ=1)64C4.127ES-(2,2)128,1724
C4.1282- 1+4 = C42.308C23central extension (φ=1)64C4.128ES-(2,2)128,1725
C4.1292- 1+4 = C42.309C23central extension (φ=1)64C4.129ES-(2,2)128,1726
C4.1302- 1+4 = C42.310C23central extension (φ=1)64C4.130ES-(2,2)128,1727
C4.1312- 1+4 = C22.50C25central extension (φ=1)64C4.131ES-(2,2)128,2193
C4.1322- 1+4 = C22.71C25central extension (φ=1)64C4.132ES-(2,2)128,2214
C4.1332- 1+4 = C22.120C25central extension (φ=1)64C4.133ES-(2,2)128,2263

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