Finite Group DatabasebetaFinite Group Databasebeta| order | 12444 |
| isoclinism | isoclinic class of C3⋊#595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C61 · Schur multiplier (H2) = C1 |
| direct product | C61×C3⋊#595 |
| unambiguous semidirect product | C3⋊(C61×#595) |
| Fitting, socle, Hall | C3×C17×C61 ⋊ C4 |
| derived, Hall | C3×C17 ⋊ C4×C61 |
| Hall | C17×C61 ⋊ Dic3 |
| Hall | C3×C61 ⋊ #595 |
| Sylow | C17 ⋊ Dic3×C61 |
| Sylow | C3 ⋊ C61×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C3⋊#595 |
| commutator, hypocenter | C3×C17 | C4×C61 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C61 | C4 |
| prime radical | C3×D17×C61 | C2 |
| cosocle | C3×D17 | C2×C61 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C61 | |
24 conjugacy classes of subgroups.
1098 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C61×C9⋊#595, C61⋊C3×C3⋊#595, C3×C61×C3⋊#595, … |
| maximal normal subgroup of | C61⋊C3×C3⋊#595, C3×C61×C3⋊#595 |
| maximal quotient of | C61×C9⋊#595, C3×C61×C3⋊#595, C61×C3⋊(C3⋊#595) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12444, 33);