Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5 |
| direct product | C3×C52×#4223 |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C4 |
| derived, Sylow | C41 ⋊ C3×C4×C52 |
| Hall | C52×C41 ⋊ C3×C4 |
| Hall | C3×C41 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | #4223 |
| commutator, hypocenter | C41 | C3×C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C4 |
| prime radical | C3×C52×D41 | C2 |
| cosocle | D41 | C2×C3×C52 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C3×C52 | |
96 conjugacy classes of subgroups.
1050 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 124);