Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ C2×M64 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×#10596842 |
| commutator, socle | C2×C73 | C22×C16 |
| Frattini | C4 | C22×#10596842 |
| Fitting | C2×C8×C73 | C8 |
| hypercenter | C2×C8 | #10596842 |
| hypocenter | C73 | C2×M64 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
112 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^10,h^c=h^72,h^d=h^27,h^e=h^72224 conjugacy classes — view the full character table.
| maximal subgroup of | #34033135, #34033138, #34033141, … |
| maximal normal subgroup of | #34033135, #34033138, #34033141, … |
| maximal quotient of | #34034379, #34034384, #34034385, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21741);