Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C73 ⋊ #1451 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#64408 |
| commutator, socle | C22×C73 | C2×C42 |
| Fitting | C22⋊C8×C73 | C4 |
| hypercenter | C22⋊C8 | #64408 |
| hypocenter | C73 | #1451 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
208 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 92 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=d,b^2=e,d^2=f,e^2=g,b^a=bg,c^a=cf,h^a=h^46,h^b=h^27,h^d=h^72,h^e=h^72416 conjugacy classes — view the full character table.
| maximal subgroup of | #34003498, #34003503, #34003508, … |
| maximal normal subgroup of | #34003498, #34003503, #34003508, … |
| maximal quotient of | #34001938, #34001959, #34003350, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 19721);