Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic188 |
| Sylow | C47 ⋊ C23×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | D188 |
| commutator | C4×C47 | C25 |
| Frattini | C4 | C24×D47 |
| Fitting | C23×C8×C47 | C2 |
| socle | C24×C47 | D4 |
| hypercenter | C23×C8 | D47 |
| hypocenter | C47 | C23×Q16 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×C8 | |
1464 conjugacy classes of subgroups.
1528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26123088, #26123090, #26123114, … |
| maximal normal subgroup of | #26123088, #26123090, #26123114, … |
| maximal quotient of | C23×#13093949, C23×#13093958, C22×C4×Dic188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 19233);