Finite Group DatabasebetaFinite Group Databasebeta| order | 5980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊#63118 |
| Fitting, socle, derived, Hall | C5×C13×C23 ⋊ C4 |
| Hall | C13×C23 ⋊ Dic5 |
| Hall | C5×C23 ⋊ #261 |
| Hall | C5×C13 ⋊ Dic23 |
| Sylow | C23 ⋊ #63118 |
| Sylow | C13 ⋊ Dic115 |
| Sylow | C5 ⋊ C23⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C13×C23 | C4 |
| LCS | G ▷ C5×C13×C23 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5,13,23|a^2=b,c^a=c^4,d^a=d^5,e^a=e^22,d^b=d^12463 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5980, 23);