Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×C47⋊#95 |
| Sylow | C47 ⋊ C4×#95 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D47 |
| commutator | C2×C47 | C43 |
| Frattini | C24 | C22×D47 |
| Fitting | C22×C42×C47 | C2 |
| socle | C24×C47 | C23 |
| hypercenter | C22×C42 | D47 |
| hypocenter | C47 | C4×#95 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C42 | |
752 conjugacy classes of subgroups.
1552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26102809, #26102836, #26102838, … |
| maximal normal subgroup of | #26102809, #26102836, #26102838, … |
| maximal quotient of | #26104197, #26104198, C4×#15688877, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2730);