Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #64408 |
| commutator, hypocenter | C73 | C4×C32 |
| Frattini | C2×C8 | C2×#64408 |
| Fitting | C2×C16×C73 | C4 |
| socle | C22×C73 | C2×C16 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C2×C16 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,h^a=h^27,h^b=h^72,h^c=h^72704 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#10596833, #34000748, #34000756, … |
| maximal normal subgroup of | C32×#10596833, #34000748, #34000756, … |
| maximal quotient of | #34000747, #34000757, #34001052, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19615);