Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C8×Q8×C73 ⋊ C2 |
| Sylow | C73 ⋊ #2982 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D73 |
| commutator | C2×C73 | C23×C8 |
| Fitting | C8×Q8×C73 | C2 |
| socle | C22×C73 | C23×C4 |
| hypercenter | C8×Q8 | D73 |
| hypocenter | C73 | #2982 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C8×Q8 | |
396 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 217 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=e,c^2=e,f^2=g,b^a=be,d^a=de,c^b=ce,h^d=h^721508 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #33055426, #33055428, #33055430, … |
| maximal normal subgroup of | #33055426, #33055428, #33055430, … |
| maximal quotient of | #33084712, #33085022, #33085023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 13589);