Finite Group DatabasebetaFinite Group Databasebeta| order | 9472 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C37 · Schur multiplier (H2) = C23 |
| direct product | C37×#8956 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C37 | #120 |
| commutator | C22×C4 | C22×C4×C37 |
| Frattini, cosocle | C2×C42 | C23×C37 |
| socle | C22×C37 | #386 |
| prime radical | C2×AGL(1,ℤ/8)×C37 | C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C37 ◁ C2×C42×C37 ◁ G | |
540 conjugacy classes of subgroups.
1924 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9472, 1944);