Finite Group DatabasebetaFinite Group Databasebeta| order | 3008 |
| isoclinism | isoclinic class of D47 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×C8×D47 |
| Fitting | C4×C8×C47 ⋊ C2 |
| derived, Sylow | C47 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D47 |
| commutator, hypocenter | C47 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D47 |
| Fitting | C4×C8×C47 | C2 |
| socle | C22×C47 | C22×C4 |
| prime radical | C22×D47 | C2×C4 |
| cosocle | C2×C4×C47 | C23 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C4×C8 | |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1504 |
800 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3008, 493);