Finite Group DatabasebetaFinite Group Databasebeta| order | 15584 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#21441261 |
| Fitting | C22×C4×C487 ⋊ C2 |
| Sylow | C487 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D487 |
| commutator, cosocle | C2×C487 | C24 |
| Frattini | C2 | C23×D487 |
| Fitting | C22×C4×C487 | C2 |
| socle | C22×C487 | C23 |
| hypercenter | C22×C4 | D487 |
| hypocenter | C487 | C2×#41 |
| LCS | G ▷ C2×C487 ▷ C487 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7792 |
3908 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44529015, #44529016, #44529018, … |
| maximal normal subgroup of | #44529015, #44529016, #44529018, … |
| maximal quotient of | C2×#29510172, C2×#29510174, C2×C4×C22⋊D487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15584, 189);