Finite Group DatabasebetaFinite Group Databasebeta| order | 9664 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#18012711 |
| Fitting | C22×D4×C151 ⋊ C2 |
| Sylow | C151 ⋊ C2×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D151 |
| commutator, cosocle | C22×C151 | C24 |
| Frattini | C22 | C23×D151 |
| Fitting | C22×D4×C151 | C2 |
| socle | C23×C151 | C23 |
| hypercenter | C22×D4 | D151 |
| hypocenter | C151 | C2×#121 |
| LCS | G ▷ C22×C151 ▷ C151 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 426 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.
1528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34069944, C4×#18012711, #34071620, … |
| maximal normal subgroup of | #34069944, C4×#18012711, #34071620, … |
| maximal quotient of | C2×#23752070, C2×#23752089, C2×#23752092, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9664, 1039);