Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16861519 |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C4 |
| derived, Hall | C52×C41 ⋊ C3×C4 |
| Hall | C3×C41 ⋊ #1043 |
| Hall | C3×C52 ⋊ #4223 |
| Sylow | C41 ⋊ C3×#1043 |
| Sylow | C52 ⋊ C3×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16861519 |
| commutator, hypocenter | C52×C41 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C4 |
| prime radical | C3×C5⋊D205 | C2 |
| cosocle | C5⋊D205 | C2×C3 |
| LCS | G ▷ C52×C41 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
780 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 133);