Finite Group DatabasebetaFinite Group Databasebeta| order | 9472 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #365 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8×C37 · Schur multiplier (H2) = C22 |
| direct product | C37×#7180 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C37 | #106 |
| commutator | C8 | C4×C8×C37 |
| Frattini, cosocle | C2×C4×C8 | C22×C37 |
| socle | C2×C37 | #1279 |
| prime radical | C23×C37 | #104 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C37 ◁ C22×C8×C37 ◁ C2×C4×C8×C37 ◁ G | |
240 conjugacy classes of subgroups.
2368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9472, 168);