Finite Group DatabasebetaFinite Group Databasebeta| order | 18382 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1313 |
| unambiguous semidirect product | C13⋊(C7×D101) |
| unambiguous semidirect product | C101⋊(C7×D13) |
| Fitting, socle, Hall | C7×C13×C101 ⋊ C2 |
| derived, Hall | C13×C101 ⋊ C2×C7 |
| Hall | C7×C101 ⋊ D13 |
| Sylow | C101 ⋊ C7×D13 |
| Hall | C7×C13 ⋊ D101 |
| Sylow | C13 ⋊ C7×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1313 |
| commutator, cosocle, hypocenter | C13×C101 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C101 | C2 |
| LCS | G ▷ C13×C101 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9191 |
4606 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#19126824, C7×#19126825, C7×D13×D101, … |
| maximal normal subgroup of | C7×#19126824, C7×#19126825, C7×D13×D101, … |
| maximal quotient of | C7×Dic1313, C2×C7×D1313 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18382, 4);