Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ #2950 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D73 |
| commutator | C4×C73 | C23×C4 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #427×C73 | C2 |
| socle | C22×C73 | C22×D4 |
| hypercenter | #427 | D73 |
| hypocenter | C73 | #2950 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ #427 | |
456 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 181 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,b^2=g,c^2=fg,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^72,d^c=dg,h^c=h^721052 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33002106, #33002110, #33002615, … |
| maximal normal subgroup of | #33002106, #33002110, #33002615, … |
| maximal quotient of | #33055457, #33055681, #33055828, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 13377);