Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C47 · Schur multiplier (H2) = C26 |
| direct product | C22×#103×C47 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C47 | D4 |
| commutator | C4 | C23×C4×C47 |
| Frattini, cosocle | C2×C4 | C24×C47 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C47 ◁ C23×C4×C47 ◁ G | |
816 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 440 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×#10789, C47×#10926, C47×#10928, … |
| maximal normal subgroup of | C47×#10789, C47×#10926, C47×#10928, … |
| maximal quotient of | C22×C47×Q8⋊C8, C2×C47×#1487, C2×C47×#1481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 1623);