Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52×C9 · Schur multiplier (H2) = C5 |
| direct product | C2×C52×#66524 |
| derived, Sylow | C37 ⋊ C2×C52×C9 |
| Hall | C2×C52×C37 ⋊ C9 |
| Hall | C52×C37 ⋊ C2×C9 |
| Hall | C2×C37 ⋊ C52×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C52 | C37⋊C3 |
| commutator, hypocenter | C37 | C2×C52×C9 |
| Frattini | C3 | C2×C52×C37⋊C3 |
| Fitting, socle, prime radical | C2×C3×C52×C37 | C3 |
| cosocle | C3×C37 | C2×C3×C52 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C3×C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16650 |
2250 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×#13050607, C5×#20269007, C5×Dic5×#66524, … |
| maximal normal subgroup of | C52×#13050607, C5×#20269007, C5×Dic5×#66524, … |
| maximal quotient of | C4×C52×#66524, C22×C52×#66524 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 51);