Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22⋊C4×D188 |
| Fitting | C4×C22⋊C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ D4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C4×C22⋊C4×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C4×C22⋊C4 | D47 |
| hypocenter | C47 | D4×C22⋊C4 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C4×C22⋊C4 | |
1252 conjugacy classes of subgroups.
970 conjugacy classes — view the full character table.
| maximal subgroup of | #26112696, #26112700, #26112724, … |
| maximal normal subgroup of | #26112696, #26112700, #26112724, … |
| maximal quotient of | C22⋊C4×(C2×D47)⋊C4, C22⋊C4×C4⋊Dic47, #95×D188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7333);