Finite Group DatabasebetaFinite Group Databasebeta| order | 37518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C37 ⋊ C2×C3 |
| Hall | C37⋊#92789 ⋊ C2 |
| Hall | C37×C13⋊D13 ⋊ C3 |
| Hall | C13⋊D13 ⋊ C37⋊C3 |
| Sylow | C132 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ #11759816 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C37 | C2×C3 |
| LCS | G ▷ C132×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1443 |
Polycyclic presentation:
2,3,13^2,37|c^a=c^12,d^a=d^12,c^b=c^3,d^b=d^9,e^b=e^261066 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37518, 77);