Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C47 · Schur multiplier (H2) = C23 |
| direct product | C47×#2048 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #394 |
| commutator, Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C2×AGL(1,ℤ/8)×C47 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G | |
274 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1081 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47×#2048, C47×#23525, C47×#24295, … |
| maximal normal subgroup of | C2×C47×#2048, C47×#23525, C47×#24295, … |
| maximal quotient of | C47×#10440, C47×#10441, C47×#10442, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 780);