Finite Group DatabasebetaFinite Group Databasebeta| order | 14916 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D33⋊D113 |
| unambiguous semidirect product | D339⋊D11 |
| unambiguous semidirect product | D1243⋊D3 |
| Fitting, socle, derived, Hall | C3×C11×C113 ⋊ C22 |
| Hall | C11×C113 ⋊ C2×D3 |
| Hall | C3×C113 ⋊ C2×D11 |
| Sylow | C113 ⋊ D3×D11 |
| Hall | C3×C11 ⋊ C2×D113 |
| Sylow | C11 ⋊ D3×D113 |
| Sylow | C3 ⋊ D11×D113 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C11×C113 | C22 |
| LCS | G ▷ C3×C11×C113 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3729 |
Polycyclic presentation:
2^2,3,11,113|d^a=d^10,e^a=e^112,c^b=c^2,d^b=d^101029 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14916, 20);