Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C47 · Schur multiplier (H2) = C23 |
| direct product | C47×#1767 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C47 | C23 |
| commutator | C22 | C2×C42×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| socle, prime radical | C23×C47 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C47 ◁ G | |
292 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2632 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#7022, C47×#7027, C47×#7041, … |
| maximal normal subgroup of | C47×#7022, C47×#7027, C47×#7041, … |
| maximal quotient of | C47×#8261, C47×#8263, C47×#8267, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 499);