Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #16861897⋊C3 |
| Fitting, socle, derived, Hall | C17×C61 ⋊ C3×C4 |
| Hall | #16861897 ⋊ C3 |
| Hall | C17×C61⋊C3 ⋊ C4 |
| Hall | C61⋊C3 ⋊ #595 |
| Sylow | C61 ⋊ C3×#595 |
| Sylow | C17 ⋊ Dic61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C61 | C3×C4 |
| prime radical | D17×C61⋊C3 | C2 |
| cosocle | D17×C61 | C2×C3 |
| LCS | G ▷ C17×C61 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,17,61|a^2=c,d^a=d^13,e^a=e^60,e^b=e^13,d^c=d^16124 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#16861897⋊C3, C3⋊(#16861897⋊C3) |
| maximal normal subgroup of | C3×#16861897⋊C3 |
| maximal quotient of | #16861897⋊C9, C3×#16861897⋊C3, C3⋊(#16861897⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 17);