Finite Group DatabasebetaFinite Group Databasebeta| order | 5730 |
| isoclinism | isoclinic class of D191 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D191 |
| Fitting, socle, Hall | C3×C5×C191 ⋊ C2 |
| derived, Sylow | C191 ⋊ C2×C3×C5 |
| Hall | C5×C191 ⋊ C2×C3 |
| Hall | C3×C191 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D191 |
| commutator, hypocenter | C191 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C191 | C2 |
| LCS | G ▷ C191 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
1455 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D191, C5×D3×D191, D15×D191, … |
| maximal normal subgroup of | C3×D5×D191, C5×D3×D191, D15×D191, … |
| maximal quotient of | C3×C5×Dic191, C2×C3×C5×D191, C5×C9×D191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5730, 3);