Finite Group DatabasebetaFinite Group Databasebeta| order | 6990 |
| automorphism | Aut(G) order 6486720 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3495 |
| unambiguous semidirect product | C3⋊D1165 |
| unambiguous semidirect product | C5⋊D699 |
| unambiguous semidirect product | C233⋊D15 |
| Fitting, socle, derived, Hall | C3×C5×C233 ⋊ C2 |
| Hall | C5×C233 ⋊ D3 |
| Hall | C3×C233 ⋊ D5 |
| Sylow | C233 ⋊ D15 |
| Hall | C3×C5 ⋊ D233 |
| Sylow | C5 ⋊ D699 |
| Sylow | C3 ⋊ D1165 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C5×C233 | C2 |
| LCS | G ▷ C3×C5×C233 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,233|b^a=b^2,c^a=c^4,d^a=d^2321749 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D15×D233, D5×D699, D3×D1165, … |
| maximal normal subgroup of | D15×D233, D5×D699, D3×D1165, … |
| maximal quotient of | Dic3495, C2×D3495, D10485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6990, 8);