Finite Group DatabasebetaFinite Group Databasebeta| order | 30448 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C42×C5×C43 (order 13760) · Inn(G) = C1 · Out(G) = C22×C42×C5×C43 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C30448 |
| abelian | C11×C16×C173 |
| multiplicative | (ℤ/30449)ˣ, (ℤ/60898)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C8 | C2×C11×C173 |
| socle, prime radical | C2×C11×C173 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
20 conjugacy classes of subgroups.
30448 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic15224, D30448 |
| maximal subgroup of | Dic15224, D30448 |
| maximal normal subgroup of | Dic15224, D30448 |
| automorphism group of | C30449 |
| outer automorphism group of | C30449 |
Past the SmallGroups library coverage — no SmallGroups id.