Finite Group DatabasebetaFinite Group Databasebeta| order | 19180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C7⋊#10587739 |
| unambiguous semidirect product | C7⋊(C5×#10587739) |
| Fitting, socle, Hall | C5×C7×C137 ⋊ C4 |
| derived, Hall | C7×C137 ⋊ C4×C5 |
| Hall | C5×C137 ⋊ Dic7 |
| Sylow | C137 ⋊ C5×Dic7 |
| Hall | C5×C7 ⋊ #10587739 |
| Sylow | C7 ⋊ C5×#10587739 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C7⋊#10587739 |
| commutator, hypocenter | C7×C137 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C137 | C4 |
| prime radical | C5×C7×D137 | C2 |
| cosocle | C7×D137 | C2×C5 |
| LCS | G ▷ C7×C137 | |
| UCS | C1 ◁ C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4795 |
1240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19180, 11);