Finite Group DatabasebetaFinite Group Databasebeta| order | 19306 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C3×C4×C7×C49 (order 8232) · Inn(G) = C1 · Out(G) = C2×C3×C4×C7×C49 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C19306 |
| abelian | C2×C49×C197 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C7 | C2×C7×C197 |
| socle, prime radical | C2×C7×C197 | C7 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
12 conjugacy classes of subgroups.
19306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C49×C197, Dic49×C197, C49×Dic197, … |
| maximal normal subgroup of | C4×C49×C197, Dic49×C197, C49×Dic197, … |
| maximal quotient of | C4×C49×C197, C22×C49×C197 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19306, 1);