Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#10625354 |
| Fitting | Q82×C47 ⋊ C2 |
| Sylow | C47 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D47 |
| commutator, socle | C22×C47 | C25 |
| Fitting | Q82×C47 | C2 |
| hypercenter | Q82 | D47 |
| hypocenter | C47 | Q8×#41 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1068 conjugacy classes of subgroups; only the 529 normal subgroups are shown.
This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 529 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
625 conjugacy classes — view the full character table.
| maximal subgroup of | #26192253, #26192261, #26192268, … |
| maximal normal subgroup of | #26192253, #26192261, #26192268, … |
| maximal quotient of | C4⋊C4×#10625354, Q8×#13093982, #26375934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 18093);