Finite Group DatabasebetaFinite Group Databasebeta| order | 3830 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D383 |
| unambiguous semidirect product | C383⋊(C2×C5) |
| Fitting, socle, Hall | C5×C383 ⋊ C2 |
| derived, Sylow | C383 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D383 |
| commutator, cosocle, hypocenter | C383 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C383 | C2 |
| LCS | G ▷ C383 | |
| UCS | C1 ◁ C5 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 388 |
| transitive degree | μt(G) = 1915 |
965 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D383, C5×D1149, C25×D383, … |
| maximal normal subgroup of | C3×C5×D383, C25×D383, C52×D383, … |
| maximal quotient of | C3×C5×D383, C5×D1149, C25×D383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3830, 2);