Finite Group DatabasebetaFinite Group Databasebeta| order | 18490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C43 · Schur multiplier (H2) = C1 |
| direct product | C5×C43×D43 |
| unambiguous semidirect product | C43⋊(C2×C5×C43) |
| Fitting, socle, Hall | C5×C432 ⋊ C2 |
| derived | C43 ⋊ C2×C5×C43 |
| Sylow | C432 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C43 | D43 |
| commutator, cosocle, hypocenter | C43 | C2×C5×C43 |
| Frattini | C1 | G |
| Fitting, socle | C5×C432 | C2 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C5×C43 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 430 |
4945 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D432, D5×C43×D43, D43×D215, … |
| maximal normal subgroup of | C5×D432, D5×C43×D43, D43×D215, … |
| maximal quotient of | C5×C43×Dic43, C2×C5×C43×D43 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18490, 10);