Finite Group DatabasebetaFinite Group Databasebeta| order | 18382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D707 |
| unambiguous semidirect product | C7⋊(C13×D101) |
| unambiguous semidirect product | C101⋊(C13×D7) |
| Fitting, socle, Hall | C7×C13×C101 ⋊ C2 |
| derived, Hall | C7×C101 ⋊ C2×C13 |
| Hall | C13×C101 ⋊ D7 |
| Sylow | C101 ⋊ C13×D7 |
| Hall | C7×C13 ⋊ D101 |
| Sylow | C7 ⋊ C13×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D707 |
| commutator, cosocle, hypocenter | C7×C101 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C101 | C2 |
| LCS | G ▷ C7×C101 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9191 |
4615 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D7×D101, D13×D707, D91⋊D101, … |
| maximal normal subgroup of | C13×D7×D101, D13×D707, D91⋊D101, … |
| maximal quotient of | C13×Dic707, C2×C13×D707 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18382, 6);