Finite Group DatabasebetaFinite Group Databasebeta| order | 3980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic199 |
| unambiguous semidirect product | C199⋊(C4×C5) |
| derived, Sylow | C199 ⋊ C4×C5 |
| Hall | C5×C199 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D199 |
| commutator, hypocenter | C199 | C4×C5 |
| Frattini | C2 | C5×D199 |
| Fitting, socle, prime radical | C2×C5×C199 | C2 |
| cosocle | C2×C199 | C2×C5 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C2×C5 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 208 |
| transitive degree | μt(G) = 3980 |
1010 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×Dic199, C5×Dic597, C5×(C199⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C5×Dic199, C5×(C199⋊C3)⋊C4, C25×Dic199, … |
| maximal quotient of | C3×C5×Dic199, C5×Dic597, C25×Dic199, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3980, 3);