Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | #10596842 |
| commutator, hypocenter | C73 | C128 |
| Fitting | C16×C73 | C8 |
| socle | C2×C73 | C64 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C16 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,73|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^10,h^b=h^27,h^c=h^72272 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#22626929, #34033166, #34033167, … |
| maximal normal subgroup of | C2×#22626929, #34033166, #34033167, … |
| maximal quotient of | #34032725, C2×#22626929 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21508);