Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C47 ⋊ #1861 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13093993 |
| commutator | C2×C4×C47 | C22×C4 |
| Frattini | C22×C4 | C22×D47 |
| Fitting | C47×#568 | C2 |
| socle | C2×C47 | #385 |
| hypercenter | #568 | D47 |
| hypocenter | C47 | #1861 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #568 | |
262 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 89 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=f,b^2=f,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^46,d^b=dg,e^c=eg814 conjugacy classes — view the full character table.
| maximal subgroup of | D47×#1861, C2×#20243628, #26217179, … |
| maximal normal subgroup of | D47×#1861, C2×#20243628, #26217179, … |
| maximal quotient of | #26110161, #26110168, #26110175, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 4750);