Finite Group DatabasebetaFinite Group Databasebeta| order | 10678 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D281 |
| unambiguous semidirect product | C281⋊(C2×C19) |
| Fitting, socle, Hall | C19×C281 ⋊ C2 |
| derived, Sylow | C281 ⋊ C2×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D281 |
| commutator, cosocle, hypocenter | C281 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C281 | C2 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C19 | |
8 conjugacy classes of subgroups.
2698 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#11765499, C19⋊#11765499, D19×D281, … |
| maximal normal subgroup of | C19×#11765499, C19⋊#11765499, D19×D281, … |
| maximal quotient of | C19×Dic281, C2×C19×D281, C3×C19×D281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10678, 2);