Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #2328 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator | C22×C73 | C23×C4 |
| Fitting | C2×#127×C73 | C2 |
| socle | C23×C73 | C24 |
| hypercenter | C2×#127 | D73 |
| hypocenter | C73 | #2328 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
740 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 237 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=g,b^2=eg,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^72,c^b=ce,h^b=h^721052 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32982681, #32982685, #32982709, … |
| maximal normal subgroup of | #32982681, #32982685, #32982709, … |
| maximal quotient of | #33007244, #33007289, #33007353, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 7236);