Finite Group DatabasebetaFinite Group Databasebeta| order | 24190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2419 |
| unambiguous semidirect product | C59⋊(C5×D41) |
| Fitting, socle, Hall | C5×C41×C59 ⋊ C2 |
| derived, Hall | C41×C59 ⋊ C2×C5 |
| Hall | C5×C59 ⋊ D41 |
| Hall | C5×C41 ⋊ D59 |
| Sylow | C59 ⋊ C5×D41 |
| Sylow | C41 ⋊ C5×D59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2419 |
| commutator, cosocle, hypocenter | C41×C59 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C41×C59 | C2 |
| LCS | G ▷ C41×C59 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12095 |
6055 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24190, 5);