Finite Group DatabasebetaFinite Group Databasebeta| order | 22272 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C4×C7×C64 (order 7168) · Inn(G) = C1 · Out(G) = C22×C4×C7×C64 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C22272 |
| abelian | C3×C29×C256 |
| multiplicative | (ℤ/22273)ˣ, (ℤ/44546)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C128 | C2×C3×C29 |
| socle, prime radical | C2×C3×C29 | C128 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
36 conjugacy classes of subgroups.
22272 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic11136, D22272 |
| maximal subgroup of | Dic11136, D22272 |
| maximal normal subgroup of | Dic11136, D22272 |
| automorphism group of | C22273 |
| outer automorphism group of | C22273 |
Past the SmallGroups library coverage — no SmallGroups id.