Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C4×#13093999 |
| Fitting | C4×C4⋊C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ C4×#121 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D47 |
| commutator | C22×C47 | C23×C4 |
| Frattini | C23 | C23×D47 |
| Fitting | C4×C4⋊C4×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C4×C4⋊C4 | D47 |
| hypocenter | C47 | C4×#121 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C4⋊C4 | |
824 conjugacy classes of subgroups.
976 conjugacy classes — view the full character table.
| maximal subgroup of | #26110808, #26110813, #26110828, … |
| maximal normal subgroup of | #26110808, #26110813, #26110828, … |
| maximal quotient of | C4×#15689001, C4×#15689015, C4×#15689024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7025);