Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×#131×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C23×D73 |
| commutator, socle | C2×C73 | C24×C4 |
| Frattini | C4 | C24×D73 |
| Fitting | C2×#131×C73 | C2 |
| hypercenter | C2×#131 | D73 |
| hypocenter | C73 | #3573 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C8 ◁ C2×#131 | |
1424 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,f^2=g,e^b=eg,d^c=dg,h^e=h^721508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33001431, #33001433, #33001434, … |
| maximal normal subgroup of | #33001431, #33001433, #33001434, … |
| maximal quotient of | #33949402, #33949403, #33949404, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19221);