Finite Group DatabasebetaFinite Group Databasebeta| order | 5820 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C97 · Schur multiplier (H2) = C1 |
| direct product | Dic15×C97 |
| unambiguous semidirect product | C3⋊(Dic5×C97) |
| derived, Hall | C3×C5 ⋊ C4×C97 |
| Hall | C3×C5×C97 ⋊ C4 |
| Hall | C5×C97 ⋊ Dic3 |
| Hall | C3×C97 ⋊ Dic5 |
| Sylow | C5 ⋊ Dic3×C97 |
| Sylow | C3 ⋊ Dic5×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C97 | D15 |
| commutator, hypocenter | C3×C5 | C4×C97 |
| Frattini | C2 | D15×C97 |
| Fitting, socle | C2×C3×C5×C97 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C2×C97 | |
24 conjugacy classes of subgroups.
1746 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C97×Dic45, Dic15×C97⋊C3, C3×Dic15×C97, … |
| maximal normal subgroup of | Dic15×C97⋊C3, C3×Dic15×C97, C5×Dic15×C97 |
| maximal quotient of | C97×Dic45, C3×Dic15×C97, C97×C3⋊Dic15, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5820, 8);