Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C47 · Schur multiplier (H2) = C22 |
| direct product | C47×#1682 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C47 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C47 |
| prime radical | #127×C47 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C47 ◁ C42×C47 ◁ G | |
166 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1363 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C47×#1682, C47×#19123, C47×#19125, … |
| maximal normal subgroup of | C2×C47×#1682, C47×#19123, C47×#19125, … |
| maximal quotient of | C47×#8649, C47×#9218, C47×#9222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 414);