Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #334×C73 ⋊ C2 |
| Sylow | C73 ⋊ #1583 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | D4×D73 |
| commutator | C2×C4×C73 | C22×C4 |
| Frattini | C42 | C22×D73 |
| Fitting | #334×C73 | C2 |
| socle | C22×C73 | C4×D4 |
| hypercenter | #334 | D73 |
| hypocenter | C73 | #1583 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2×C4 ◁ C42 ◁ #334 | |
166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,d^b=df,h^b=h^72,h^c=h^721046 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1583×D73, C2×#22608773, #33055510, … |
| maximal normal subgroup of | #1583×D73, C2×#22608773, #33055510, … |
| maximal quotient of | #32976780, #32976829, #32977267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 3352);