Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C47×#477 ⋊ C2 |
| Sylow | C47 ⋊ #3357 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#477 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #477 | D47 |
| hypocenter | C47 | #3357 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #477 | |
354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=eg,b^2=g,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=dg,f^a=fg,c^b=cg,d^b=de,h^b=h^46,f^c=fg,h^d=h^46466 conjugacy classes — view the full character table.
| maximal subgroup of | #26207208, #26207210, #26207253, … |
| maximal normal subgroup of | #26207208, #26207210, #26207253, … |
| maximal quotient of | #26232724, #26232741, #26234013, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17133);