Finite Group DatabasebetaFinite Group Databasebeta| order | 37278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#32916124 |
| Fitting, socle, Hall | C2×C19×C109 ⋊ C9 |
| derived, Hall | C19×C109 ⋊ C2×C9 |
| Hall | C2×C109 ⋊ #4296 |
| Sylow | C109 ⋊ C2×#4296 |
| Hall | C2×C19 ⋊ #11758281 |
| Sylow | C19 ⋊ C2×#11758281 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #32916124 |
| commutator, hypocenter | C19×C109 | C2×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C109 | C9 |
| prime radical | C2×#20261879 | C3 |
| cosocle | #20261879 | C2×C3 |
| LCS | G ▷ C19×C109 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4142 |
478 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37278, 68);