Finite Group DatabasebetaFinite Group Databasebeta| order | 34050 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | C52⋊C3×D227 |
| unambiguous semidirect product | C227⋊(C2×C52⋊C3) |
| unambiguous semidirect product | (C52×D227)⋊C3 |
| Fitting, socle, derived, Hall | C52×C227 ⋊ C2×C3 |
| Hall | C52⋊C3×C227 ⋊ C2 |
| Hall | C52×D227 ⋊ C3 |
| Sylow | C227 ⋊ C2×C52⋊C3 |
| Sylow | C52 ⋊ C3×D227 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C227 | C2×C3 |
| LCS | G ▷ C52×C227 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3405 |
1265 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34050, 10);