Finite Group DatabasebetaFinite Group Databasebeta| order | 18450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C41 · Schur multiplier (H2) = C3 |
| direct product | C32×C41×D25 |
| unambiguous semidirect product | C25⋊(C2×C32×C41) |
| Fitting, Hall | C32×C25×C41 ⋊ C2 |
| derived, Sylow | C25 ⋊ C2×C32×C41 |
| Hall | C25×C41 ⋊ C2×C32 |
| Hall | C32×C25 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C41 | D25 |
| commutator, cosocle, hypocenter | C25 | C2×C32×C41 |
| Frattini | C5 | C32×D5×C41 |
| Fitting | C32×C25×C41 | C2 |
| socle | C32×C5×C41 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C32×C41 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9225 |
5166 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C41×#1035, C32×#16861482, C32×D25×D41, … |
| maximal normal subgroup of | C32×C41×#1035, C32×#16861482, C32×D25×D41, … |
| maximal quotient of | C32×C41×Dic25, C2×C32×C41×D25 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18450, 21);