Finite Group DatabasebetaFinite Group Databasebeta| order | 20332 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#11725133 |
| Fitting, socle, Hall | C13×C17×C23 ⋊ C4 |
| derived, Hall | C13×C17 ⋊ C4×C23 |
| Hall | C17×C23 ⋊ Dic13 |
| Hall | C13×C23 ⋊ #595 |
| Sylow | C17 ⋊ C23×Dic13 |
| Sylow | C13 ⋊ C23×#595 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #11725133 |
| commutator, hypocenter | C13×C17 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C13×C17×C23 | C4 |
| prime radical | C13×C23×D17 | C2 |
| cosocle | C13×D17 | C2×C23 |
| LCS | G ▷ C13×C17 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5083 |
1564 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20332, 22);