Finite Group DatabasebetaFinite Group Databasebeta| order | 3904 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×#6923 |
| Fitting | M16×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#6923 |
| commutator, socle | C2×C61 | C2×C42 |
| Fitting | M16×C61 | C4 |
| prime radical | C22×D61 | C2×C4 |
| cosocle | C4×D61 | C23 |
| hypercenter | M16 | #6923 |
| hypocenter | C61 | C4×M16 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C4 ◁ M16 | |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 488 |
190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3904, 1509);