Finite Group DatabasebetaFinite Group Databasebeta| order | 28170 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C313 · Schur multiplier (H2) = C1 |
| direct product | C3×D15×C313 |
| unambiguous semidirect product | C3⋊(C3×D5×C313) |
| unambiguous semidirect product | C5⋊(C3×D3×C313) |
| Fitting, socle, Hall | C32×C5×C313 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C3×C313 |
| Hall | C32×C313 ⋊ D5 |
| Hall | C5×C313 ⋊ C3×D3 |
| Hall | C32×C5 ⋊ C2×C313 |
| Sylow | C32 ⋊ D5×C313 |
| Sylow | C5 ⋊ C3×D3×C313 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C313 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C3×C313 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C313 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C313 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9390 |
8451 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28170, 27);