Finite Group DatabasebetaFinite Group Databasebeta| order | 13650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D455 |
| unambiguous semidirect product | C5⋊(C3×C5×D91) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D455 |
| commutator, cosocle, hypocenter | C5×C7×C13 | C2×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C13 | C2 |
| LCS | G ▷ C5×C7×C13 | |
| UCS | C1 ◁ C3×C5 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2730 |
3435 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D13×D35, C3×C5×D7×D65, C3×C5×D5×D91, … |
| maximal normal subgroup of | C3×C5×D13×D35, C3×C5×D7×D65, C3×C5×D5×D91, … |
| maximal quotient of | C3×C5×Dic455, C2×C3×C5×D455 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13650, 158);