Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | M16×Dic94 |
| Sylow | C47 ⋊ Q8×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D47 |
| commutator, socle | C22×C47 | C23×C4 |
| Fitting | C4×M16×C47 | C2 |
| hypercenter | C4×M16 | D47 |
| hypocenter | C47 | Q8×M16 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
388 conjugacy classes of subgroups.
970 conjugacy classes — view the full character table.
| maximal subgroup of | #26110612, #26110616, #26110626, … |
| maximal normal subgroup of | #26110612, #26110616, #26110626, … |
| maximal quotient of | M16×C4⋊Dic47, M16×Dic47⋊C4, #26214927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13463);