Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C8×C47⋊C16 |
| derived, Sylow | C47 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C82 | D47 |
| commutator, hypocenter | C47 | C8×C16 |
| Frattini | C4×C8 | C2×D47 |
| Fitting | C82×C47 | C2 |
| socle | C22×C47 | C4×C8 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C82 | |
104 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×C47⋊C16, #26102892, #26102893, … |
| maximal normal subgroup of | C16×C47⋊C16, #26102892, #26102893, … |
| maximal quotient of | C16×C47⋊C16, #26102892, #26103106, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2425);