Finite Group DatabasebetaFinite Group Databasebeta| order | 16198 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C89 · Schur multiplier (H2) = C1 |
| direct product | C7×D13×C89 |
| unambiguous semidirect product | C13⋊(C2×C7×C89) |
| Fitting, socle, Hall | C7×C13×C89 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C7×C89 |
| Hall | C13×C89 ⋊ C2×C7 |
| Hall | C7×C13 ⋊ C2×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C89 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C7×C89 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C89 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C7×C89 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8099 |
4984 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#261×C89, C7×#17987774, C7×D13×D89, … |
| maximal normal subgroup of | C7×#261×C89, C7×#17987774, C7×D13×D89, … |
| maximal quotient of | C7×Dic13×C89, C2×C7×D13×C89 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16198, 3);