Finite Group DatabasebetaFinite Group Databasebeta| order | 16650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C37⋊C3×(C5⋊D5)⋊C3 |
| unambiguous semidirect product | (C5⋊D5×C37⋊C3)⋊C3 |
| unambiguous semidirect product | (C37×(C5⋊D5)⋊C3)⋊C3 |
| unambiguous semidirect product | ((C5⋊D5)⋊(C37⋊C3))⋊C3 |
| Fitting, socle, derived, Hall | C52×C37 ⋊ C2×C32 |
| Hall | C52⋊C3×C37⋊C3 ⋊ C2 |
| Hall | C37×C5⋊D5 ⋊ C32 |
| Hall | C5⋊D5 ⋊ C3×C37⋊C3 |
| Sylow | C37 ⋊ C3×(C5⋊D5)⋊C3 |
| Sylow | C52 ⋊ C2×C3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C37 | C2×C32 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 555 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | (C5⋊D5)⋊C3×D37⋊C3, #26012847⋊C3, C37⋊C3×#64480, … |
| maximal normal subgroup of | (C5⋊D5)⋊C3×D37⋊C3, #26012847⋊C3, C37⋊C3×#64480, … |
| maximal quotient of | C37⋊C3×#1039⋊C3, C2×C37⋊C3×(C5⋊D5)⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16650, 76);