Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C2×C4 |
| direct product | C8×#10625329 |
| Sylow | C47 ⋊ C8×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C8 | C2×D47 |
| commutator | C2×C47 | C2×C4×C8 |
| Frattini | C42 | C22×D47 |
| Fitting | C2×C4×C8×C47 | C2 |
| socle | C22×C47 | C2×C42 |
| hypercenter | C2×C4×C8 | D47 |
| hypocenter | C47 | C8×M16 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4×C8 ◁ C2×C4×C8 | |
224 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26103168, #26103169, #26103174, … |
| maximal normal subgroup of | #26103168, #26103169, #26103174, … |
| maximal quotient of | C8×#13093935, #26105660, #26106704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 2790);