Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29×C4 |
| direct product | C22×#14556587 |
| Fitting | C23×D4×C73 ⋊ C2 |
| Sylow | C73 ⋊ C22×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D73 |
| commutator | C22×C73 | C25 |
| Frattini | C22 | C24×D73 |
| Fitting | C23×D4×C73 | C2 |
| socle | C24×C73 | C23 |
| hypercenter | C23×D4 | D73 |
| hypocenter | C73 | C22×#127 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
3000 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 3000 conjugacy classes of subgroups — too many to draw. Only its 725 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1496 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32978600, #32992519, #32992520, … |
| maximal normal subgroup of | #32978600, #32992519, #32992520, … |
| maximal quotient of | C22×#17988456, C22×#17988487, C22×#17988488, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17781);