Finite Group DatabasebetaFinite Group Databasebeta| order | 9472 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C37 · Schur multiplier (H2) = C24 |
| direct product | C37×#12586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C37 | C2×#99 |
| commutator | C2×C4 | C2×C42×C37 |
| Frattini, cosocle | C22×Q8 | C23×C37 |
| prime radical | C24×C37 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C37 ◁ C24×C37 ◁ C23×Q8×C37 ◁ G | |
746 conjugacy classes of subgroups.
1702 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9472, 5574);