Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #454×D73 |
| Fitting | #454×C73 ⋊ C2 |
| Sylow | C73 ⋊ C2×#454 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #120×D73 |
| commutator | C2×C4×C73 | C24 |
| Frattini | C2×C4 | C23×D73 |
| Fitting | #454×C73 | C2 |
| socle | C2×C73 | C2×#120 |
| hypercenter | #454 | D73 |
| hypocenter | C73 | C2×#454 |
| LCS | G ▷ C2×C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #454 | |
728 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
608 conjugacy classes — view the full character table.
| maximal subgroup of | #1404×D73, #33006237, #2202×D73, … |
| maximal normal subgroup of | #1404×D73, #33006237, #2202×D73, … |
| maximal quotient of | #1597×D73, #1615×D73, #1598×D73, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 13843);