Finite Group DatabasebetaFinite Group Databasebeta| order | 3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | M32×D47 |
| Fitting | M32×C47 ⋊ C2 |
| Sylow | C47 ⋊ C2×M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D47 |
| commutator, socle | C2×C47 | C22×C8 |
| Fitting | M32×C47 | C2 |
| prime radical | C22×D47 | C8 |
| cosocle | C8×C47 | C23 |
| hypercenter | M32 | D47 |
| hypocenter | C47 | C2×M32 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C8 ◁ M32 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 752 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3008, 962);