Finite Group DatabasebetaFinite Group Databasebeta| order | 9324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C37 ⋊ C4×C9 |
| Hall | #14556422 ⋊ C4 |
| Hall | Dic7×C37 ⋊ C9 |
| Sylow | C37 ⋊ Dic7⋊C9 |
| Hall | Dic7 ⋊ #66526 |
| Sylow | C7 ⋊ C4×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #17987954 |
| commutator, hypocenter | C7×C37 | C4×C9 |
| Fitting, socle | C2×C7×C37 | C2×C9 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,37,2|a^2=f,b^3=c,d^a=d^6,d^b=d^2,e^b=e^16,e^c=e^2682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9324, 81);