Finite Group DatabasebetaFinite Group Databasebeta| order | 3450 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D5×C23 |
| unambiguous semidirect product | C5⋊(C2×C3×C5×C23) |
| Fitting, socle, Hall | C3×C52×C23 ⋊ C2 |
| derived | C5 ⋊ C2×C3×C5×C23 |
| Hall | C52×C23 ⋊ C2×C3 |
| Hall | C3×C52 ⋊ C2×C23 |
| Sylow | C52 ⋊ C2×C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C23 | D5 |
| commutator, cosocle, hypocenter | C5 | C2×C3×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C23 | C2 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C3×C5×C23 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 690 |
1380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3450, 17);