Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Sylow | C73 ⋊ #1744 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×#64408 |
| commutator | C2×C73 | C2×C4×C8 |
| Frattini | C23 | C22×#64408 |
| Fitting | C2×C42×C73 | C4 |
| socle | C23×C73 | C22×C4 |
| hypercenter | C2×C42 | #64408 |
| hypocenter | C73 | #1744 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
296 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 142 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=e,b^2=f,c^2=d,e^2=g,b^a=bd,h^a=h^27,h^c=h^72,h^e=h^72656 conjugacy classes — view the full character table.
| maximal subgroup of | #33999897, #33999921, #33999928, … |
| maximal normal subgroup of | #33999897, #33999921, #33999928, … |
| maximal quotient of | #34003346, #34003348, #34003352, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20225);