Finite Group DatabasebetaFinite Group Databasebeta| order | 9372 |
| isoclinism | isoclinic class of D71 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×C11×Dic71 |
| unambiguous semidirect product | C71⋊(C3×C4×C11) |
| derived, Sylow | C71 ⋊ C3×C4×C11 |
| Hall | C3×C11×C71 ⋊ C4 |
| Hall | C11×C71 ⋊ C3×C4 |
| Hall | C3×C71 ⋊ C4×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C11 | D71 |
| commutator, hypocenter | C71 | C3×C4×C11 |
| Frattini | C2 | C3×C11×D71 |
| Fitting, socle | C2×C3×C11×C71 | C2 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C3×C11 | |
24 conjugacy classes of subgroups.
2442 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×C11×Dic71, C3×C11×Dic213, C32×C11×Dic71 |
| maximal normal subgroup of | C9×C11×Dic71, C32×C11×Dic71 |
| maximal quotient of | C9×C11×Dic71, C3×C11×Dic213, C32×C11×Dic71 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9372, 2);