Finite Group DatabasebetaFinite Group Databasebeta| order | 6990 |
| isoclinism | isoclinic class of D233 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D233 |
| unambiguous semidirect product | C233⋊(C2×C3×C5) |
| Fitting, socle, Hall | C3×C5×C233 ⋊ C2 |
| derived, Sylow | C233 ⋊ C2×C3×C5 |
| Hall | C5×C233 ⋊ C2×C3 |
| Hall | C3×C233 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D233 |
| commutator, hypocenter | C233 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C233 | C2 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C3×C5 | |
16 conjugacy classes of subgroups.
1770 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×#11745400, C3×#17987920, C3×D5×D233, … |
| maximal normal subgroup of | C3×C5×#11745400, C3×#17987920, C3×D5×D233, … |
| maximal quotient of | C3×C5×Dic233, C2×C3×C5×D233, C5×C9×D233, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6990, 2);