Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | D8×C73 ⋊ C8 |
| Sylow | C73 ⋊ #1580 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#10596842 |
| commutator | C4×C73 | C22×C8 |
| Frattini | C4 | C22×#10596842 |
| Fitting | D8×C73 | C8 |
| socle | C2×C73 | C8×D4 |
| hypercenter | D8 | #10596842 |
| hypocenter | C73 | #1580 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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,c^2=ef,d^2=f,e^2=g,b^a=bd,c^a=cf,d^a=df,h^a=h^63,d^b=df,h^c=h^10,h^e=h^27,h^g=h^72107 conjugacy classes — view the full character table.
| maximal subgroup of | #34034018, #34034019, #34034022, … |
| maximal normal subgroup of | #34034018, #34034019, #34034022, … |
| maximal quotient of | #34033279, #34033294, #34033359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 21641);