Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C22×#13093964 |
| Sylow | C47 ⋊ C22×M32 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8 | C2×D47 |
| commutator | C2×C47 | C23×C8 |
| Frattini | C8 | C23×D47 |
| Fitting | C23×C8×C47 | C2 |
| socle | C23×C47 | C2×C8 |
| hypercenter | C23×C8 | D47 |
| hypocenter | C47 | C22×M32 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C8 ◁ C23×C8 | |
400 conjugacy classes of subgroups.
1552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26131117, #26131118, #26131120, … |
| maximal normal subgroup of | #26131117, #26131118, #26131120, … |
| maximal quotient of | C22×#15688899, C2×C4×#13093964, C22×C22⋊(C47⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17606);