Finite Group DatabasebetaFinite Group Databasebeta| order | 9472 |
| nilpotency class | 5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C37 · Schur multiplier (H2) = C2 |
| direct product | C37×#7378 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C37 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C2×C8×C37 |
| Frattini, cosocle | #408 | C22×C37 |
| socle | C2×C37 | #1326 |
| prime radical | C2×#41×C37 | C2×C4 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C37 ◁ C2×C4×C37 ◁ C22×C4×C37 ◁ C37×#408 ◁ G | |
170 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1258 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9472, 366);