Finite Group DatabasebetaFinite Group Databasebeta| order | 30450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C29 · Schur multiplier (H2) = C1 |
| direct product | C7×C29×#3874 |
| Fitting, socle, Hall | C52×C7×C29 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2×C7×C29 |
| Hall | C7×C29×C52⋊C3 ⋊ C2 |
| Hall | C29×C52⋊C3 ⋊ C2×C7 |
| Hall | C52×C29 ⋊ D3×C7 |
| Hall | C7×C52⋊C3 ⋊ C2×C29 |
| Hall | C52×C7 ⋊ D3×C29 |
| Sylow | C52 ⋊ D3×C7×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C29 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C2×C7×C29 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C29 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C7×C29 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3045 |
2639 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30450, 58);