Finite Group DatabasebetaFinite Group Databasebeta| order | 27072 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C23×C3×C16×C23 (order 8832) · Inn(G) = C1 · Out(G) = C23×C3×C16×C23 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C27072 |
| abelian | C9×C47×C64 |
| multiplicative | (ℤ/27073)ˣ, (ℤ/54146)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C32 | C2×C3×C47 |
| socle, prime radical | C2×C3×C47 | C3×C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
42 conjugacy classes of subgroups.
27072 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic13536, D27072 |
| maximal subgroup of | Dic13536, D27072 |
| maximal normal subgroup of | Dic13536, D27072 |
| automorphism group of | C27073 |
| outer automorphism group of | C27073 |
Past the SmallGroups library coverage — no SmallGroups id.