Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | #117×Dic47 |
| Sylow | C47 ⋊ C4×#117 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D47 |
| commutator | C2×C47 | C22×C42 |
| Frattini | C23 | C23×D47 |
| Fitting | C2×#117×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×#117 | D47 |
| hypocenter | C47 | C4×#117 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C2×#117 | |
752 conjugacy classes of subgroups.
1000 conjugacy classes — view the full character table.
| maximal subgroup of | #26109719, #26109723, H(3,ℤ/4)×Dic47, … |
| maximal normal subgroup of | #26109719, #26109723, H(3,ℤ/4)×Dic47, … |
| maximal quotient of | #376×Dic47, C4×C22⋊C4×Dic47, C4×C4⋊C4×Dic47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6853);