Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C22×#14556565 |
| Fitting | C24×C4×C73 ⋊ C2 |
| Sylow | C73 ⋊ C22×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D73 |
| commutator | C22×C73 | C25 |
| Frattini | C22 | C24×D73 |
| Fitting | C24×C4×C73 | C2 |
| socle | C24×C73 | C23 |
| hypercenter | C24×C4 | D73 |
| hypocenter | C73 | C22×#121 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C24×C4 | |
2528 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 2528 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.
2360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #32977340, #32977424, #32977426, … |
| maximal normal subgroup of | #32977340, #32977424, #32977426, … |
| maximal quotient of | C22×#17988447, C22×#17988466, C22×#17988478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 17732);