Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#16861896 |
| Fitting, socle, derived, Hall | C3×C17×C61 ⋊ C4 |
| Hall | C17×C61 ⋊ Dic3 |
| Hall | C3×C61 ⋊ #595 |
| Sylow | C61 ⋊ C3⋊#595 |
| Hall | C3×C17 ⋊ #6923 |
| Sylow | C17 ⋊ C3⋊#6923 |
| Sylow | C3 ⋊ #16861896 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C17×C61 | C4 |
| prime radical, cosocle | C3×D1037 | C2 |
| LCS | G ▷ C3×C17×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17,61|a^2=b,c^a=c^2,d^a=d^13,e^a=e^11,d^b=d^16,e^b=e^60783 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16861896, C3⋊(#16861896⋊C3), C3×C3⋊#16861896, … |
| maximal normal subgroup of | C3⋊(#16861896⋊C3), C3×C3⋊#16861896 |
| maximal quotient of | C9⋊#16861896, C3×C3⋊#16861896, C3⋊(C3⋊#16861896) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 35);