Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| isoclinism | isoclinic class of Dic94 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C24×D188 |
| Fitting | C24×C4×C47 ⋊ C2 |
| Sylow | C47 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C25 | C2×D47 |
| commutator | C2×C47 | C26 |
| Frattini | C2 | C25×D47 |
| Fitting | C24×C4×C47 | C2 |
| socle | C25×C47 | C22 |
| hypercenter | C24×C4 | D47 |
| hypocenter | C47 | C24×D4 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C25 ◁ C24×C4 | |
10552 conjugacy classes of subgroups.
1552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#20241628, #26138147, #26138493, … |
| maximal normal subgroup of | C2×#20241628, #26138147, #26138493, … |
| maximal quotient of | C24×(C2×D47)⋊C4, C24×C4⋊Dic47, C23×C4×D188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 19303);