Finite Group DatabasebetaFinite Group Databasebeta| order | 9472 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C2 |
| direct product | C37×#12075 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C37 | C2×D8 |
| commutator | C2×C8 | C22×C4×C37 |
| Frattini, cosocle | C4×C8 | C23×C37 |
| socle | C22×C37 | C4×D8 |
| prime radical | C2×D8×C37 | C2×C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C37 ◁ C4×C8×C37 ◁ C82×C37 ◁ G | |
224 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2146 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9472, 5063);