Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C73 ⋊ C2×#504 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#10596842 |
| commutator, socle | C2×C73 | C23×C8 |
| Frattini | C2 | C23×#10596842 |
| Fitting | #41×C73 | C8 |
| hypercenter | #41 | #10596842 |
| hypocenter | C73 | C2×#504 |
| LCS | G ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C4 ◁ #41 | |
368 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 189 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=e,e^2=f,f^2=g,h^a=h^10,c^b=cg,h^d=h^72,h^e=h^27,h^f=h^72170 conjugacy classes — view the full character table.
| maximal subgroup of | #34034114, #34034117, #34034278, … |
| maximal normal subgroup of | #34034114, #34034117, #34034278, … |
| maximal quotient of | #34034670, C4×#17989708, C4×#17989709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21761);