Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | Q8×(C2×D47)⋊C4 |
| Fitting | C2×C4×Q8×C47 ⋊ C2 |
| Sylow | C47 ⋊ Q8×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C2×C4×Q8×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×C4×Q8 | D47 |
| hypocenter | C47 | Q8×C22⋊C4 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
820 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 287 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
970 conjugacy classes — view the full character table.
| maximal subgroup of | #26231991, #26231992, #26232021, … |
| maximal normal subgroup of | #26231991, #26231992, #26232021, … |
| maximal quotient of | C4⋊C4×(C2×D47)⋊C4, Q8×C47⋊#95, #26137819, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7343);