Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#10596842 |
| commutator, socle | C2×C73 | C22×C16 |
| Fitting | #41×C73 | C8 |
| hypercenter | #41 | #10596842 |
| hypocenter | C73 | #2258 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ #41 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^10,c^b=cg,h^d=h^27,h^e=h^72170 conjugacy classes — view the full character table.
| maximal subgroup of | #34034467, #34034468, #34034470, … |
| maximal normal subgroup of | #34034467, #34034468, #34034470, … |
| maximal quotient of | #34034387, #34034407, #34034428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21743);