Finite Group DatabasebetaFinite Group Databasebeta| order | 18733 |
| automorphism | ? |
| homology | Abelianization (H1) = C11×C13 · Schur multiplier (H2) = C1 |
| direct product | C11×C131⋊C13 |
| unambiguous semidirect product | C131⋊(C11×C13) |
| unambiguous semidirect product | (C11×C131)⋊C13 |
| Fitting, socle, Hall | C11×C131 ⋊ C13 |
| derived, Sylow | C131 ⋊ C11×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C131⋊C13 |
| commutator, cosocle, hypocenter | C131 | C11×C13 |
| Frattini | C1 | G |
| Fitting, socle | C11×C131 | C13 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1441 |
253 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C11×C131⋊C13, C11×D131⋊C13, D11×C131⋊C13, … |
| maximal normal subgroup of | C2×C11×C131⋊C13, C11×D131⋊C13, D11×C131⋊C13, … |
| maximal quotient of | C2×C11×C131⋊C13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18733, 1);