Finite Group DatabasebetaFinite Group Databasebeta| order | 22372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C47⋊#595 |
| unambiguous semidirect product | C47⋊(C7×#595) |
| Fitting, socle, Hall | C7×C17×C47 ⋊ C4 |
| derived, Hall | C17×C47 ⋊ C4×C7 |
| Hall | C7×C47 ⋊ #595 |
| Hall | C7×C17 ⋊ Dic47 |
| Sylow | C47 ⋊ C7×#595 |
| Sylow | C17 ⋊ C7×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C47⋊#595 |
| commutator, hypocenter | C17×C47 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C17×C47 | C4 |
| prime radical | C7×D17×C47 | C2 |
| cosocle | D17×C47 | C2×C7 |
| LCS | G ▷ C17×C47 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5593 |
1666 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22372, 11);