Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| direct product | D13×C3⋊(C11⋊D11) |
| unambiguous semidirect product | (C3×D13)⋊(C11⋊D11) |
| unambiguous semidirect product | (C11×D13)⋊D33 |
| Fitting, socle, derived, Hall | C3×C112×C13 ⋊ C22 |
| Hall | C112×C13 ⋊ C2×D3 |
| Hall | C3×C112 ⋊ C2×D13 |
| Sylow | C112 ⋊ D3×D13 |
| Hall | C3×C13 ⋊ C2×C11⋊D11 |
| Sylow | C13 ⋊ C2×C3⋊(C11⋊D11) |
| Sylow | C3 ⋊ D13×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C112×C13 | C22 |
| LCS | G ▷ C3×C112×C13 | |
| UCS | C1 | |
280 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4719 |
1464 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 135);