Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14556641 |
| Sylow | C73 ⋊ C22⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×#64408 |
| commutator | C2×C73 | C2×C32 |
| Fitting | C22×C8×C73 | C4 |
| socle | C22×C73 | C2×C16 |
| hypercenter | C22×C8 | #64408 |
| hypocenter | C73 | C22⋊C32 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C8 ◁ C22×C8 | |
82 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^27,h^d=h^72656 conjugacy classes — view the full character table.
| maximal subgroup of | #34000767, #34000768, #34000769, … |
| maximal normal subgroup of | #34000767, #34000768, #34000769, … |
| maximal quotient of | #34000767, #34000827, D4⋊#14556641, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19623);