Finite Group DatabasebetaFinite Group Databasebeta| order | 18490 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C43 |
| unambiguous semidirect product | C5⋊(C43⋊D43) |
| unambiguous semidirect product | C43⋊D215 |
| Fitting, socle, derived, Hall | C5×C432 ⋊ C2 |
| Sylow | C432 ⋊ D5 |
| Sylow | C5 ⋊ C43⋊D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C432 | C2 |
| LCS | G ▷ C5×C432 | |
| UCS | C1 | |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9245 |
Polycyclic presentation:
2,5,43^2|b^a=b^4,c^a=c^42,d^a=d^424624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49149748, D43×D215, D5×C43⋊D43, … |
| maximal normal subgroup of | #49149748, D43×D215, D5×C43⋊D43, … |
| maximal quotient of | C43⋊Dic215, C2×C5⋊(C43⋊D43) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18490, 6);