Finite Group DatabasebetaFinite Group Databasebeta| order | 5980 |
| isoclinism | isoclinic class of #261 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×C23×#261 |
| Fitting, socle, Hall | C5×C13×C23 ⋊ C4 |
| derived, Sylow | C13 ⋊ C4×C5×C23 |
| Hall | C13×C23 ⋊ C4×C5 |
| Hall | C5×C13 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C23 | #261 |
| commutator, hypocenter | C13 | C4×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C13×C23 | C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C5×C23 | |
24 conjugacy classes of subgroups.
805 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5980, 10);