Finite Group Databasebeta

Complete groups

Centerless groups whose automorphisms are all inner — each one canonically isomorphic to its own automorphism group.

ordergroupconjugacy classessolvable
6D3 #73✓
20AGL(1,𝔽5) #525✓
24S4 #715✓
42AGL(1,𝔽7) #1837✓
54AGL(1,ℤ/9) #27010✓
110AGL(1,𝔽11) #112011✓
120S5 #12247–
120D3×AGL(1,𝔽5) #122615✓
144AΓL(1,𝔽9) #38399✓
144D3×S4 #384015✓
156AGL(1,𝔽13) #391013✓
168AΓL(1,𝔽8) #42738✓
216((C22⋊C9)⋊C2)⋊C3 #625319✓
252D3×AGL(1,𝔽7) #698721✓
272AGL(1,𝔽17) #6326317✓
320#6629711✓
324D3×AGL(1,ℤ/9) #6642630✓
336SO(3,𝔽7) #667399–
342AGL(1,𝔽19) #6678919✓
384#4626⋊C2 #7310116✓
384#4625⋊C2 #7310216✓
432#6249⋊C2 #8887314✓
432((C3⋊S4)⋊C3)⋊C2 #8887620✓
432AGL(2,𝔽3) #8908711✓
480AGL(1,𝔽5)×S4 #9211325✓
486AGL(1,ℤ/27) #9218631✓
500AGL(1,ℤ/25) #9253226✓
506AGL(1,𝔽23) #9277923✓
1296#10620184⋊C2 #1304977222✓
1320PGL(2,𝔽11) #1305042913–
1440PΓL(2,𝔽9) #1308952413–
2184PGL(2,𝔽13) #7221035615–
4896PGL(2,𝔽17) #7221036119–
5040S7 #7221020915–
6840PGL(2,𝔽19) #7221036621–
7920M11 #7220963410–
12144PGL(2,𝔽23) #7221037225–
24360PGL(2,𝔽29) #7221038631–
29760PGL(2,𝔽31) #7221038933–
40320S8 #7221021022–
50616PGL(2,𝔽37) #7221040039–
58968PΓL(2,𝔽27) #7222446623–

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