Finite Group DatabasebetaFinite Group Databasebeta| order | 26980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic71⋊C5 |
| unambiguous semidirect product | Dic71⋊(C5×C19) |
| unambiguous semidirect product | (C71⋊C5)⋊(C4×C19) |
| unambiguous semidirect product | (C19×Dic71)⋊C5 |
| derived, Sylow | C71 ⋊ C4×C5×C19 |
| Hall | C19×C71⋊C5 ⋊ C4 |
| Hall | C19×Dic71 ⋊ C5 |
| Hall | C19×C71 ⋊ C4×C5 |
| Hall | C71⋊C5 ⋊ C4×C19 |
| Hall | Dic71 ⋊ C5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D71⋊C5 |
| commutator, hypocenter | C71 | C4×C5×C19 |
| Frattini | C2 | C19×D71⋊C5 |
| Fitting, socle | C2×C19×C71 | C2×C5 |
| prime radical | C2×C19×C71⋊C5 | C2 |
| cosocle | C2×C71 | C2×C5×C19 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5396 |
646 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26980, 10);