Finite Group DatabasebetaFinite Group Databasebeta| order | 16550 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C2×C5×C331⋊C5 |
| unambiguous semidirect product | (C2×C331)⋊C52 |
| unambiguous semidirect product | (C2×C5×C331)⋊C5 |
| Fitting, socle | C2×C5×C331 ⋊ C5 |
| derived, Sylow | C331 ⋊ C2×C52 |
| Hall | C2×C331 ⋊ C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | C331⋊C5 |
| commutator, cosocle, hypocenter | C331 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C331 | C5 |
| LCS | G ▷ C331 | |
| UCS | C1 ◁ C2×C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3310 |
710 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic331⋊C5, (C331⋊C5)⋊Dic5, Dic5×C331⋊C5, … |
| maximal normal subgroup of | C5×Dic331⋊C5, (C331⋊C5)⋊Dic5, Dic5×C331⋊C5, … |
| maximal quotient of | C4×C5×C331⋊C5, C22×C5×C331⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16550, 11);