Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C73 ⋊ #2501 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D73 |
| commutator, socle | C23×C73 | C24 |
| Fitting | C2×#121×C73 | C2 |
| hypercenter | C2×#121 | D73 |
| hypocenter | C73 | #2501 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C2×#121 | |
708 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 708 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=g,b^2=e,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^72,c^b=cg,h^c=h^721046 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32983725, #32986444, #32986448, … |
| maximal normal subgroup of | #32983725, #32986444, #32986448, … |
| maximal quotient of | #33007970, #33008216, #33009108, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 8982);