Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D73⋊#436 |
| Sylow | C73 ⋊ C2×#436 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#64408 |
| commutator, socle | C22×C73 | C23×C4 |
| Frattini | C22 | C23×#64408 |
| Fitting | C4×D4×C73 | C4 |
| hypercenter | C4×D4 | #64408 |
| hypocenter | C73 | C2×#436 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
552 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=f,c^2=f,f^2=g,b^a=be,c^a=cg,h^a=h^46,c^b=cg,h^c=h^27,h^d=h^72,h^f=h^72416 conjugacy classes — view the full character table.
| maximal subgroup of | #34003673, #34003681, #34003689, … |
| maximal normal subgroup of | #34003673, #34003681, #34003689, … |
| maximal quotient of | D73⋊#1589, D73⋊#1590, D73⋊#1591, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21223);