Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14556641 |
| Sylow | C73 ⋊ C4⋊C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×#64408 |
| commutator | C2×C73 | C2×C32 |
| Fitting | C4×C8×C73 | C4 |
| socle | C22×C73 | C2×C16 |
| hypercenter | C4×C8 | #64408 |
| hypocenter | C73 | C4⋊C32 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=d,b^2=c,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 | D4⋊#14556641, #34000864, #34000865, … |
| maximal normal subgroup of | D4⋊#14556641, #34000864, #34000865, … |
| maximal quotient of | #34001027, #34001035, #34001051, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19667);