Finite Group DatabasebetaFinite Group Databasebeta| order | 24910 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D2491 |
| unambiguous semidirect product | C47⋊(C5×D53) |
| unambiguous semidirect product | C53⋊(C5×D47) |
| Fitting, socle, Hall | C5×C47×C53 ⋊ C2 |
| derived, Hall | C47×C53 ⋊ C2×C5 |
| Hall | C5×C53 ⋊ D47 |
| Hall | C5×C47 ⋊ D53 |
| Sylow | C53 ⋊ C5×D47 |
| Sylow | C47 ⋊ C5×D53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D2491 |
| commutator, cosocle, hypocenter | C47×C53 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C47×C53 | C2 |
| LCS | G ▷ C47×C53 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12455 |
6235 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24910, 4);