Finite Group DatabasebetaFinite Group Databasebeta| order | 37278 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C109 ⋊ C2×C9 |
| Hall | #32916114 ⋊ C2 |
| Hall | D19×C109 ⋊ C9 |
| Sylow | C109 ⋊ #4294⋊C2 |
| Hall | D19 ⋊ #11758279 |
| Sylow | C19 ⋊ C2×#11758279 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #27159096 |
| commutator, hypocenter | C19×C109 | C2×C9 |
| Fitting, socle, cosocle | C3×C19×C109 | C2×C3 |
| prime radical | C3×D19×C109 | C3 |
| LCS | G ▷ C19×C109 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18639 |
Polycyclic presentation:
2,3,19,109,3|b^3=e,c^a=c^18,c^b=c^7,d^b=d^451215 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37278, 20);