Finite Group DatabasebetaFinite Group Databasebeta| order | 18490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C43 |
| direct product | C5×C43⋊D43 |
| unambiguous semidirect product | C43⋊(C5×D43) |
| Fitting, socle, Hall | C5×C432 ⋊ C2 |
| derived, Sylow | C432 ⋊ C2×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C43⋊D43 |
| commutator, cosocle, hypocenter | C432 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C432 | C2 |
| LCS | G ▷ C432 | |
| UCS | C1 ◁ C5 | |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9245 |
4630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×#20301711, C5×D432, #49149752, … |
| maximal normal subgroup of | C5×#20301711, C5×D432, #49149752, … |
| maximal quotient of | C5×C43⋊Dic43, C2×C5×C43⋊D43 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18490, 9);