Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of C3⋊#1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×C3⋊#1043 |
| unambiguous semidirect product | C3⋊(C41×#1043) |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C4 |
| derived, Hall | C3×C52 ⋊ C4×C41 |
| Hall | C52×C41 ⋊ Dic3 |
| Hall | C3×C41 ⋊ #1043 |
| Sylow | C52 ⋊ Dic3×C41 |
| Sylow | C3 ⋊ C41×#1043 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | C3⋊#1043 |
| commutator, hypocenter | C3×C52 | C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C4 |
| prime radical | C3×C41×C5⋊D5 | C2 |
| cosocle | C3×C5⋊D5 | C2×C41 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C41 | |
96 conjugacy classes of subgroups.
984 conjugacy classes — view the full character table.
| maximal subgroup of | C41×C9⋊#1043, C41×C3⋊(#1043⋊C3), C3×C41×C3⋊#1043, … |
| maximal normal subgroup of | C41×C3⋊(#1043⋊C3), C3×C41×C3⋊#1043 |
| maximal quotient of | C41×C9⋊#1043, C3×C41×C3⋊#1043, C41×C3⋊(C3⋊#1043) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 159);