Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C47 ⋊ #2949 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D47 |
| commutator | C4×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#518 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #518 | D47 |
| hypocenter | C47 | #2949 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #518 | |
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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=g,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,e^b=eg,h^b=h^46,d^c=dg826 conjugacy classes — view the full character table.
| maximal subgroup of | #26230180, #26230182, #26232188, … |
| maximal normal subgroup of | #26230180, #26230182, #26232188, … |
| maximal quotient of | #26185741, #26185956, #26185967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13367);