Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C73 ⋊ #1985 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#64408 |
| commutator, socle | C23×C73 | C22×C4 |
| Fitting | C22×Q8×C73 | C4 |
| hypercenter | C22×Q8 | #64408 |
| hypocenter | C73 | #1985 |
| LCS | G ▷ C23×C73 ▷ C73 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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=def,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^46,c^b=cg,h^b=h^27,h^c=h^72,h^f=h^72404 conjugacy classes — view the full character table.
| maximal subgroup of | #34000732, #34004521, #34004523, … |
| maximal normal subgroup of | #34000732, #34004521, #34004523, … |
| maximal quotient of | #34008105, #34008108, #34008111, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 20684);