Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C73 ⋊ C8 |
| Sylow | C73 ⋊ #2982 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#10596842 |
| commutator, socle | C2×C73 | C23×C8 |
| Fitting | C2×Q8×C73 | C8 |
| hypercenter | C2×Q8 | #10596842 |
| hypocenter | C73 | #2982 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
396 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 191 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,h^a=h^10,c^b=ce,h^f=h^27,h^g=h^72158 conjugacy classes — view the full character table.
| maximal subgroup of | #34033354, #34033373, #34033375, … |
| maximal normal subgroup of | #34033354, #34033373, #34033375, … |
| maximal quotient of | #34034548, #34034551, #34034585, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21753);