Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C47 · Schur multiplier (H2) = C24 |
| direct product | C47×#1896 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C47 | C2×D4 |
| commutator | C2×C4 | C22×C4×C47 |
| Frattini, cosocle | C22×C4 | C23×C47 |
| socle | C22×C47 | C2×C22⋊C4 |
| prime radical | C47×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C47 ◁ C23×C4×C47 ◁ G | |
442 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 120 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C47×#8346, C47×#8347, C2×C47×#1896, … |
| maximal normal subgroup of | C47×#8346, C47×#8347, C2×C47×#1896, … |
| maximal quotient of | C47×#9071, C47×#9072, C47×#9077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 628);