Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23 |
| direct product | C22×C47⋊C32 |
| derived, Sylow | C47 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | D47 |
| commutator, hypocenter | C47 | C22×C32 |
| Frattini | C16 | C22×D47 |
| Fitting | C22×C16×C47 | C2 |
| socle | C23×C47 | C16 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C22×C16 | |
120 conjugacy classes of subgroups.
1600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26103964, #26103965, #26103976, … |
| maximal normal subgroup of | #26103964, #26103965, #26103976, … |
| maximal quotient of | C2×C4×C47⋊C32, C2×C22⋊(C47⋊C32), C2×C4⋊(C47⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6799);