Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ C2×#346 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×#10596842 |
| commutator | C2×C73 | C2×C4×C8 |
| Frattini | C22 | C22×#10596842 |
| Fitting | C42×C73 | C8 |
| socle | C22×C73 | C22×C8 |
| hypercenter | C42 | #10596842 |
| hypocenter | C73 | C2×#346 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
200 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bg,h^a=h^10,h^c=h^72,h^d=h^27,h^f=h^72224 conjugacy classes — view the full character table.
| maximal subgroup of | #34032858, #34032910, #34032919, … |
| maximal normal subgroup of | #34032858, #34032910, #34032919, … |
| maximal quotient of | #34033477, #34033488, #34033503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21666);