Finite Group DatabasebetaFinite Group Databasebeta| order | 24156 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | D671⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C11×C61 ⋊ C22 |
| Hall | C11×C61 ⋊ C2×C3⋊D3 |
| Hall | C32×C61 ⋊ C2×D11 |
| Hall | C32×C11 ⋊ C2×D61 |
| Sylow | C61 ⋊ C3⋊D3×D11 |
| Sylow | C11 ⋊ C3⋊D3×D61 |
| Sylow | C32 ⋊ D11×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C11×C61 | C22 |
| LCS | G ▷ C32×C11×C61 | |
| UCS | C1 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6039 |
Polycyclic presentation:
2^2,3^2,11,61|e^a=e^10,f^a=f^60,c^b=c^2,d^b=d^2,e^b=e^101572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24156, 115);