Finite Group DatabasebetaFinite Group Databasebeta| order | 9924 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic827 |
| unambiguous semidirect product | C827⋊(C3×C4) |
| derived, Sylow | C827 ⋊ C3×C4 |
| Hall | C3×C827 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D827 |
| commutator, hypocenter | C827 | C3×C4 |
| Frattini | C2 | C3×D827 |
| Fitting, socle, prime radical | C2×C3×C827 | C2 |
| cosocle | C2×C827 | C2×C3 |
| LCS | G ▷ C827 | |
| UCS | C1 ◁ C2×C3 | |
12 conjugacy classes of subgroups.
2490 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×Dic827, C3×Dic2481, C32×Dic827 |
| maximal normal subgroup of | C9×Dic827, C32×Dic827 |
| maximal quotient of | C9×Dic827, C3×Dic2481, C32×Dic827 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9924, 3);