Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#14556519 |
| Fitting | C43×C73 ⋊ C2 |
| Sylow | C73 ⋊ C4×#104 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | D292 |
| commutator | C4×C73 | C2×C42 |
| Frattini | C22×C4 | C22×D73 |
| Fitting | C43×C73 | C2 |
| socle | C22×C73 | C2×C22⋊C4 |
| hypercenter | C43 | D73 |
| hypocenter | C73 | C4×#104 |
| LCS | G ▷ C4×C73 ▷ C2×C73 ▷ C73 | |
| UCS | C1 ◁ C42 ◁ C2×C42 ◁ C43 | |
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32976689, C8×#14556519, #32976696, … |
| maximal normal subgroup of | #32976689, C8×#14556519, #32976696, … |
| maximal quotient of | C4×#17988316, C4×#17988319, #32976597, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 4316);