Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #442×C73 ⋊ C2 |
| Sylow | C73 ⋊ #3401 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #442×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #442 | D73 |
| hypocenter | C73 | #3401 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
368 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|b^2=e,c^2=e,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^72,c^b=cg,d^b=de,h^b=h^72,f^c=fg,h^d=h^72821 conjugacy classes — view the full character table.
| maximal subgroup of | #3401×D73, C2×#22623002, #33967022, … |
| maximal normal subgroup of | #3401×D73, C2×#22623002, #33967022, … |
| maximal quotient of | #33102860, #33102871, #33104862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17581);