Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C73 ⋊ #3573 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×#64408 |
| commutator, socle | C2×C73 | C24×C4 |
| Fitting | H(5,𝔽2)×C73 | C4 |
| hypercenter | H(5,𝔽2) | #64408 |
| hypocenter | C73 | #3573 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,73|a^2=f,f^2=g,h^a=h^27,e^b=eg,d^c=dg,h^f=h^72374 conjugacy classes — view the full character table.
| maximal subgroup of | #34022882, #34022884, #34022886, … |
| maximal normal subgroup of | #34022882, #34022884, #34022886, … |
| maximal quotient of | #34031091, #34031092, #34031121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21505);