Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×Dic183 |
| unambiguous semidirect product | C3⋊(C17×Dic61) |
| derived, Hall | C3×C61 ⋊ C4×C17 |
| Hall | C3×C17×C61 ⋊ C4 |
| Hall | C17×C61 ⋊ Dic3 |
| Sylow | C61 ⋊ Dic3×C17 |
| Hall | C3×C17 ⋊ Dic61 |
| Sylow | C3 ⋊ C17×Dic61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | D183 |
| commutator, hypocenter | C3×C61 | C4×C17 |
| Frattini | C2 | C17×D183 |
| Fitting, socle, prime radical | C2×C3×C17×C61 | C2 |
| cosocle | C2×C3×C61 | C2×C17 |
| LCS | G ▷ C3×C61 | |
| UCS | C1 ◁ C2×C17 | |
24 conjugacy classes of subgroups.
3162 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×Dic549, C17×C3⋊(Dic61⋊C3), C17×C3⋊Dic183, … |
| maximal normal subgroup of | C17×C3⋊(Dic61⋊C3), C3×C17×Dic183 |
| maximal quotient of | C17×Dic549, C17×C3⋊Dic183, C3×C17×Dic183 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 7);