Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | Q8×C47⋊C16 |
| Sylow | C47 ⋊ Q8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D47 |
| commutator | C2×C47 | C22×C16 |
| Fitting | C8×Q8×C47 | C2 |
| socle | C22×C47 | C22×C8 |
| hypercenter | C8×Q8 | D47 |
| hypocenter | C47 | Q8×C16 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
134 conjugacy classes of subgroups.
1000 conjugacy classes — view the full character table.
| maximal subgroup of | #26128041, SD16×C47⋊C16, #26128055, … |
| maximal normal subgroup of | #26128041, SD16×C47⋊C16, #26128055, … |
| maximal quotient of | C4⋊C4×C47⋊C16, #26133895, #26134279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6414);