Finite Group DatabasebetaFinite Group Databasebeta| order | 16498 |
| isoclinism | isoclinic class of D113 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×D113 |
| unambiguous semidirect product | C113⋊(C2×C73) |
| Fitting, socle, Hall | C73×C113 ⋊ C2 |
| derived, Sylow | C113 ⋊ C2×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | D113 |
| commutator, cosocle, hypocenter | C113 | C2×C73 |
| Frattini | C1 | G |
| Fitting, socle | C73×C113 | C2 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C73 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8249 |
4234 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C73×#90673, #45682486, D73×D113, … |
| maximal normal subgroup of | C73×#90673, #45682486, D73×D113, … |
| maximal quotient of | C73×Dic113, C2×C73×D113 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16498, 2);