Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C47 · Schur multiplier (H2) = C24 |
| direct product | C47×#2009 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C47 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C47 |
| prime radical | C47×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C47 ◁ C22×C4×C47 ◁ G | |
348 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 88 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×#2009, C47×#23412, C47×#23873, … |
| maximal normal subgroup of | C2×C47×#2009, C47×#23412, C47×#23873, … |
| maximal quotient of | C47×#9931, C47×#9933, C47×#9935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 741);