Finite Group DatabasebetaFinite Group Databasebeta| order | 3700 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic185 |
| derived | C5×C37 ⋊ C4×C5 |
| Hall | C52×C37 ⋊ C4 |
| Sylow | C37 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ Dic37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D185 |
| commutator, hypocenter | C5×C37 | C4×C5 |
| Frattini | C2 | C5×D185 |
| Fitting, socle, prime radical | C2×C52×C37 | C2 |
| cosocle | C2×C5×C37 | C2×C5 |
| LCS | G ▷ C5×C37 | |
| UCS | C1 ◁ C2×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 740 |
940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic185⋊C3, #26012787, C3×C5×Dic185, … |
| maximal normal subgroup of | C5×Dic185⋊C3, C3×C5×Dic185, C5×C7×Dic185 |
| maximal quotient of | C3×C5×Dic185, C5×Dic555, C5×Dic1295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3700, 19);