Finite Group DatabasebetaFinite Group Databasebeta| order | 7518 |
| automorphism | Aut(G) order 8029224 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D3759 |
| unambiguous semidirect product | C3⋊D1253 |
| unambiguous semidirect product | C7⋊D537 |
| unambiguous semidirect product | C179⋊D21 |
| Fitting, socle, derived, Hall | C3×C7×C179 ⋊ C2 |
| Hall | C7×C179 ⋊ D3 |
| Hall | C3×C179 ⋊ D7 |
| Sylow | C179 ⋊ D21 |
| Hall | C3×C7 ⋊ D179 |
| Sylow | C7 ⋊ D537 |
| Sylow | C3 ⋊ D1253 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C7×C179 | C2 |
| LCS | G ▷ C3×C7×C179 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,179|b^a=b^2,c^a=c^6,d^a=d^1781881 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D21×D179, D7×D537, D3×D1253, … |
| maximal normal subgroup of | D21×D179, D7×D537, D3×D1253, … |
| maximal quotient of | Dic3759, C2×D3759, D11277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7518, 9);