Finite Group DatabasebetaFinite Group Databasebeta| order | 9344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#17988443 |
| Sylow | C73 ⋊ C2×#379 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D73 |
| commutator | C22×C73 | C23×C4 |
| Frattini | C23 | C23×D73 |
| Fitting | C26×C73 | C2 |
| socle | C24×C73 | C23 |
| hypercenter | C26 | D73 |
| hypocenter | C73 | C2×#379 |
| LCS | G ▷ C22×C73 ▷ C73 | |
| UCS | C1 ◁ C24 ◁ C26 | |
3464 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 549 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 | C2×#22607835, #32976308, #32991245, … |
| maximal normal subgroup of | C2×#22607835, #32976308, #32991245, … |
| maximal quotient of | C2×#22608154, C4×#17988443, C2×#22608172, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9344, 6878);