Finite Group DatabasebetaFinite Group Databasebeta| order | 18380 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D919 |
| unambiguous semidirect product | C919⋊(C22×C5) |
| unambiguous semidirect product | (C2×C919)⋊(C2×C5) |
| Fitting, socle | C2×C5×C919 ⋊ C2 |
| derived, Sylow | C919 ⋊ C22×C5 |
| Hall | C5×C919 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D919 |
| commutator, cosocle, hypocenter | C919 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C919 | C2 |
| LCS | G ▷ C919 | |
| UCS | C1 ◁ C2×C5 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9190 |
4610 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18380, 11);