Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C47×#504 ⋊ C2 |
| Sylow | C47 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C23×D47 |
| commutator, socle | C2×C47 | C23×C8 |
| Fitting | C47×#504 | C2 |
| hypercenter | #504 | D47 |
| hypocenter | C47 | #3407 |
| LCS | G ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C8 ◁ #504 | |
360 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 209 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=e,e^2=f,f^2=g,d^a=dg,c^b=cg,h^d=h^46988 conjugacy classes — view the full character table.
| maximal subgroup of | #26369521, #26369524, #26369528, … |
| maximal normal subgroup of | #26369521, #26369524, #26369528, … |
| maximal quotient of | #26368916, #26368926, #26368927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 17611);