Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D51⋊D61 |
| unambiguous semidirect product | D183⋊D17 |
| unambiguous semidirect product | D1037⋊D3 |
| Fitting, socle, derived, Hall | C3×C17×C61 ⋊ C22 |
| Hall | C17×C61 ⋊ C2×D3 |
| Hall | C3×C61 ⋊ C2×D17 |
| Sylow | C61 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ C2×D61 |
| Sylow | C17 ⋊ D3×D61 |
| Sylow | C3 ⋊ D17×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C61 | C22 |
| LCS | G ▷ C3×C17×C61 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17,61|d^a=d^16,e^a=e^60,c^b=c^2,d^b=d^16840 conjugacy classes — view the full character table.
| maximal subgroup of | D153⋊D61, D51⋊(D61⋊C3), C3×D51⋊D61, … |
| maximal normal subgroup of | D51⋊(D61⋊C3), C3×D51⋊D61 |
| maximal quotient of | D153⋊D61, C3×D51⋊D61, D183⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 42);