Frobenius groups
Groups G = K ⋊ H whose complement H meets each of its conjugates trivially.
| order | group | splitting |
|---|
| 6 | D3 #7 | C3 ⋊ C2 |
| 10 | D5 #17 | C5 ⋊ C2 |
| 12 | A4 #22 | C22 ⋊ C3 |
| 14 | D7 #26 | C7 ⋊ C2 |
| 18 | D9 #44 | C9 ⋊ C2 |
| 18 | C3⋊D3 #47 | C32 ⋊ C2 |
| 20 | AGL(1,𝔽5) #52 | C5 ⋊ C4 |
| 21 | ΓL(1,𝔽8) #55 | C7 ⋊ C3 |
| 22 | D11 #57 | C11 ⋊ C2 |
| 26 | D13 #77 | C13 ⋊ C2 |
| 30 | D15 #91 | C3×C5 ⋊ C2 |
| 34 | D17 #146 | C17 ⋊ C2 |
| 36 | #157 | C32 ⋊ C4 |
| 38 | D19 #164 | C19 ⋊ C2 |
| 39 | C13⋊C3 #166 | C13 ⋊ C3 |
| 42 | AGL(1,𝔽7) #183 | C7 ⋊ C2×C3 |
| 42 | D21 #187 | C3×C7 ⋊ C2 |
| 46 | D23 #196 | C23 ⋊ C2 |
| 48 | C42⋊C3 #201 | C42 ⋊ C3 |
| 48 | C22⋊A4 #248 | C24 ⋊ C3 |
| 50 | D25 #253 | C25 ⋊ C2 |
| 50 | C5⋊D5 #256 | C52 ⋊ C2 |
| 52 | #261 | C13 ⋊ C4 |
| 54 | D27 #265 | C27 ⋊ C2 |
| 54 | C3⋊D9 #271 | C3×C9 ⋊ C2 |
| 54 | C3⋊(C3⋊D3) #278 | C33 ⋊ C2 |
| 55 | C11⋊C5 #280 | C11 ⋊ C5 |
| 56 | AGL(1,𝔽8) #292 | C23 ⋊ C7 |
| 57 | C19⋊C3 #295 | C19 ⋊ C3 |
| 58 | D29 #297 | C29 ⋊ C2 |
| 62 | D31 #314 | C31 ⋊ C2 |
| 66 | D33 #590 | C3×C11 ⋊ C2 |
| 68 | #595 | C17 ⋊ C4 |
| 70 | D35 #601 | C5×C7 ⋊ C2 |
| 72 | AGL(1,𝔽9) #642 | C32 ⋊ C8 |
| 72 | PSU(3,𝔽2) #644 | C32 ⋊ Q8 |
| 74 | D37 #655 | C37 ⋊ C2 |
| 75 | C52⋊C3 #658 | C52 ⋊ C3 |
| 78 | D13⋊C3 #665 | C13 ⋊ C2×C3 |
| 78 | D39 #669 | C3×C13 ⋊ C2 |
| 80 | C24⋊C5 #720 | C24 ⋊ C5 |
| 82 | D41 #739 | C41 ⋊ C2 |
| 84 | C22⋊ΓL(1,𝔽8) #752 | C22×C7 ⋊ C3 |
| 86 | D43 #758 | C43 ⋊ C2 |
| 90 | D45 #776 | C5×C9 ⋊ C2 |
| 90 | C3⋊D15 #782 | C32×C5 ⋊ C2 |
| 93 | C31⋊C3 #789 | C31 ⋊ C3 |
| 94 | D47 #791 | C47 ⋊ C2 |
| 98 | D49 #1026 | C49 ⋊ C2 |
| 98 | C7⋊D7 #1029 | C72 ⋊ C2 |
| 100 | #1035 | C25 ⋊ C4 |
| 100 | #1043 | C52 ⋊ C4 |
| 100 | #1044 | C52 ⋊ C4 |
| 102 | D51 #1052 | C3×C17 ⋊ C2 |
| 106 | D53 #1071 | C53 ⋊ C2 |
| 110 | AGL(1,𝔽11) #1120 | C11 ⋊ C2×C5 |
| 110 | D55 #1124 | C5×C11 ⋊ C2 |
| 111 | C37⋊C3 #1126 | C37 ⋊ C3 |
| 114 | D19⋊C3 #1172 | C19 ⋊ C2×C3 |
| 114 | D57 #1176 | C3×C19 ⋊ C2 |
| 116 | #1181 | C29 ⋊ C4 |
| 118 | D59 #1188 | C59 ⋊ C2 |
| 122 | D61 #1240 | C61 ⋊ C2 |
| 126 | D63 #1256 | C7×C9 ⋊ C2 |
| 126 | C3⋊D21 #1266 | C32×C7 ⋊ C2 |
| 129 | C43⋊C3 #3597 | C43 ⋊ C3 |
| 130 | D65 #3601 | C5×C13 ⋊ C2 |
| 134 | D67 #3615 | C67 ⋊ C2 |
| 136 | #3633 | C17 ⋊ C8 |
| 138 | D69 #3640 | C3×C23 ⋊ C2 |
| 142 | D71 #3655 | C71 ⋊ C2 |
| 146 | D73 #3856 | C73 ⋊ C2 |
| 147 | C49⋊C3 #3858 | C49 ⋊ C3 |
| 147 | #3861 | C72 ⋊ C3 |
| 147 | #3862 | C72 ⋊ C3 |
| 148 | #3866 | C37 ⋊ C4 |
| 150 | D75 #3872 | C3×C25 ⋊ C2 |
| 150 | (C5⋊D5)⋊C3 #3875 | C52 ⋊ C2×C3 |
| 150 | C3⋊(C5⋊D5) #3881 | C3×C52 ⋊ C2 |
| 154 | D77 #3900 | C7×C11 ⋊ C2 |
| 155 | ΓL(1,𝔽32) #3902 | C31 ⋊ C5 |
| 156 | AGL(1,𝔽13) #3910 | C13 ⋊ C3×C4 |
| 156 | C22⋊(C13⋊C3) #3917 | C22×C13 ⋊ C3 |
| 158 | D79 #3923 | C79 ⋊ C2 |
| 162 | D81 #4165 | C81 ⋊ C2 |
| 162 | C9⋊D9 #4180 | C92 ⋊ C2 |
| 162 | C3⋊D27 #4182 | C3×C27 ⋊ C2 |
| 162 | C3⋊(C3⋊D9) #4209 | C32×C9 ⋊ C2 |
| 162 | C3⋊(C3⋊(C3⋊D3)) #4218 | C34 ⋊ C2 |
| 164 | #4223 | C41 ⋊ C4 |
| 166 | D83 #4228 | C83 ⋊ C2 |
| 170 | D85 #4292 | C5×C17 ⋊ C2 |
| 171 | #4296 | C19 ⋊ C9 |
| 174 | D87 #4306 | C3×C29 ⋊ C2 |
| 178 | D89 #4353 | C89 ⋊ C2 |
| 180 | #4380 | C32×C5 ⋊ C4 |
| 182 | D91 #4396 | C7×C13 ⋊ C2 |
| 183 | C61⋊C3 #4398 | C61 ⋊ C3 |
| 186 | D31⋊C3 #4413 | C31 ⋊ C2×C3 |
| 186 | D93 #4417 | C3×C31 ⋊ C2 |
About Frobenius groups →
Finite Group Databasebeta