Finite Group DatabasebetaFinite Group Databasebeta| order | 5820 |
| isoclinism | isoclinic class of D97 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×Dic97 |
| derived, Sylow | C97 ⋊ C3×C4×C5 |
| Hall | C3×C5×C97 ⋊ C4 |
| Hall | C5×C97 ⋊ C3×C4 |
| Hall | C3×C97 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | D97 |
| commutator, hypocenter | C97 | C3×C4×C5 |
| Frattini | C2 | C3×C5×D97 |
| Fitting, socle | C2×C3×C5×C97 | C2 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C2×C3×C5 | |
24 conjugacy classes of subgroups.
1500 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C9×Dic97, C5×Dic97⋊C9, C3×C5×Dic97⋊C3, … |
| maximal normal subgroup of | C5×C9×Dic97, C5×Dic97⋊C9, C3×C5×Dic97⋊C3, … |
| maximal quotient of | C5×C9×Dic97, C32×C5×Dic97, C3×C5×Dic291, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5820, 3);