Finite Group DatabasebetaFinite Group Databasebeta| order | 2220 |
| isoclinism | isoclinic class of #10625194⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10625194⋊C3 |
| Fitting, socle, derived, Hall | C5×C37 ⋊ C3×C4 |
| Hall | #10625194 ⋊ C3 |
| Hall | C5×C37⋊C3 ⋊ C4 |
| Hall | C37⋊C3 ⋊ Dic5 |
| Sylow | C37 ⋊ C3×Dic5 |
| Sylow | C5 ⋊ #3866⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C37 | C3×C4 |
| prime radical | C5×D37⋊C3 | C2 |
| cosocle | C5×D37 | C2×C3 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 42 |
| transitive degree | μt(G) = 185 |
Polycyclic presentation:
2,3,2,5,37|a^2=c,d^a=d^4,e^a=e^31,e^b=e^26,e^c=e^3639 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2220, 19);