Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×#10625354 |
| Fitting | D4×Q8×C47 ⋊ C2 |
| Sylow | C47 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | D4×Q8×C47 | C2 |
| hypercenter | D4×Q8 | D47 |
| hypocenter | C47 | D4×#41 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ D4×Q8 | |
1648 conjugacy classes of subgroups.
625 conjugacy classes — view the full character table.
| maximal subgroup of | #26192227, #26192235, #26192242, … |
| maximal normal subgroup of | #26192227, #26192235, #26192242, … |
| maximal quotient of | C22⋊C4×#10625354, C4⋊C4×#10625354, D4×#13093982, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 18002);