Finite Group DatabasebetaFinite Group Databasebeta| order | 30688 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C22×C3×C82×C17 (order 13056) · Inn(G) = C1 · Out(G) = C22×C3×C82×C17 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C30688 |
| abelian | C7×C32×C137 |
| multiplicative | (ℤ/30689)ˣ, (ℤ/61378)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C16 | C2×C7×C137 |
| socle, prime radical | C2×C7×C137 | C16 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
24 conjugacy classes of subgroups.
30688 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | Dic15344, D30688 |
| maximal subgroup of | Dic15344, D30688 |
| maximal normal subgroup of | Dic15344, D30688 |
| automorphism group of | C30689 |
| outer automorphism group of | C30689 |
Past the SmallGroups library coverage — no SmallGroups id.