Finite Group DatabasebetaFinite Group Databasebeta| order | 20332 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#11725133 |
| Fitting, socle, derived, Hall | C13×C17×C23 ⋊ C4 |
| Hall | C17×C23 ⋊ Dic13 |
| Hall | C13×C23 ⋊ #595 |
| Hall | C13×C17 ⋊ Dic23 |
| Sylow | C23 ⋊ #11725133 |
| Sylow | C17 ⋊ Dic299 |
| Sylow | C13 ⋊ C23⋊#595 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C17×C23 | C4 |
| prime radical, cosocle | C13×C23×D17 | C2 |
| LCS | G ▷ C13×C17×C23 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5083 |
Polycyclic presentation:
2^2,13,17,23|a^2=b,c^a=c^12,d^a=d^13,e^a=e^22,d^b=d^161498 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20332, 23);