Finite Group DatabasebetaFinite Group Databasebeta| order | 18518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C197 · Schur multiplier (H2) = C1 |
| direct product | D47×C197 |
| unambiguous semidirect product | C47⋊(C2×C197) |
| Fitting, socle, Hall | C47×C197 ⋊ C2 |
| derived, Sylow | C47 ⋊ C2×C197 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C197 | D47 |
| commutator, cosocle, hypocenter | C47 | C2×C197 |
| Frattini | C1 | G |
| Fitting, socle | C47×C197 | C2 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C197 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9259 |
4925 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D47×D197, C2×D47×C197 |
| maximal normal subgroup of | D47×D197, C2×D47×C197 |
| maximal quotient of | Dic47×C197, C2×D47×C197 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18518, 1);