Finite Group DatabasebetaFinite Group Databasebeta| order | 13620 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5×C227 · Schur multiplier (H2) = C1 |
| direct product | C5×Dic3×C227 |
| unambiguous semidirect product | C3⋊(C4×C5×C227) |
| derived, Sylow | C3 ⋊ C4×C5×C227 |
| Hall | C3×C5×C227 ⋊ C4 |
| Hall | C3×C227 ⋊ C4×C5 |
| Hall | C3×C5 ⋊ C4×C227 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C227 | D3 |
| commutator, hypocenter | C3 | C4×C5×C227 |
| Frattini | C2 | C5×D3×C227 |
| Fitting, socle, prime radical | C2×C3×C5×C227 | C2 |
| cosocle | C2×C3 | C2×C5×C227 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C5×C227 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13620 |
6810 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13620, 5);