Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C3×#19149851 |
| Fitting, socle | C3×C52×C37 ⋊ C2×C3 |
| derived, Hall | C52×C37 ⋊ C2×C32 |
| Hall | C3×C52⋊(C37⋊C3) ⋊ C2 |
| Hall | C5⋊D185 ⋊ C32 |
| Sylow | C37 ⋊ C3×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C3×D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #19149851 |
| commutator, cosocle, hypocenter | C52×C37 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C2×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1665 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D37⋊((C5⋊D5)⋊C3), C3×#26012838, C3×#26012839, … |
| maximal normal subgroup of | C3×D37⋊((C5⋊D5)⋊C3), C3×#26012838, C3×#26012839, … |
| maximal quotient of | C3×#26012789, C2×C3×#19149851 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 90);