Finite Group DatabasebetaFinite Group Databasebeta| order | 24850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C71 · Schur multiplier (H2) = C5 |
| direct product | C71×C5⋊D35 |
| unambiguous semidirect product | C5⋊(D35×C71) |
| unambiguous semidirect product | C7⋊(C5⋊D5×C71) |
| Fitting, socle, Hall | C52×C7×C71 ⋊ C2 |
| derived, Hall | C52×C7 ⋊ C2×C71 |
| Hall | C52×C71 ⋊ D7 |
| Hall | C7×C71 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ D7×C71 |
| Sylow | C7 ⋊ C5⋊D5×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | C5⋊D35 |
| commutator, cosocle, hypocenter | C52×C7 | C2×C71 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C71 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C71 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12425 |
6319 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24850, 47);