Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C3×C41×#1042 |
| Fitting, socle, Hall | C3×C52×C41 ⋊ C4 |
| derived, Sylow | C52 ⋊ C3×C4×C41 |
| Hall | C52×C41 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ C4×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C41 | #1042 |
| commutator, hypocenter | C52 | C3×C4×C41 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C41 | C4 |
| prime radical | C3×C5×D5×C41 | C2 |
| cosocle | C5×D5 | C2×C3×C41 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C41 | |
52 conjugacy classes of subgroups.
1599 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C41×#1042, C32×C41×#1042, C3×C41×C3⋊#1042 |
| maximal normal subgroup of | C9×C41×#1042, C32×C41×#1042 |
| maximal quotient of | C9×C41×#1042, C32×C41×#1042, C3×C41×C3⋊#1042 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 138);