Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C4×Q8×Dic47 |
| Sylow | C47 ⋊ C42×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D47 |
| commutator | C2×C47 | C22×C42 |
| Frattini | C23 | C23×D47 |
| Fitting | C2×C4×Q8×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×C4×Q8 | D47 |
| hypocenter | C47 | C42×Q8 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C4×Q8 | |
684 conjugacy classes of subgroups; only the 425 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 425 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1000 conjugacy classes — view the full character table.
| maximal subgroup of | Q8⋊C8×Dic47, #26106887, #26106897, … |
| maximal normal subgroup of | Q8⋊C8×Dic47, #26106887, #26106897, … |
| maximal quotient of | C4×C4⋊C4×Dic47, C4×#15689009, #387×Dic47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 6861);