Finite Group DatabasebetaFinite Group Databasebeta| order | 18650 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D373 |
| unambiguous semidirect product | C373⋊(C2×C52) |
| Fitting, socle, Hall | C52×C373 ⋊ C2 |
| derived, Sylow | C373 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D373 |
| commutator, cosocle, hypocenter | C373 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C373 | C2 |
| LCS | G ▷ C373 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9325 |
4700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×#13093637, C5×#21418654, C5×D5×D373, … |
| maximal normal subgroup of | C52×#13093637, C5×#21418654, C5×D5×D373, … |
| maximal quotient of | C52×Dic373, C2×C52×D373 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18650, 10);