Finite Group DatabasebetaFinite Group Databasebeta| order | 24850 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(C7⋊(D71⋊C5)) |
| unambiguous semidirect product | C7⋊(C5⋊(D71⋊C5)) |
| unambiguous semidirect product | (C71⋊C5)⋊D35 |
| unambiguous semidirect product | D2485⋊C5 |
| Fitting, socle, derived | C5×C7×C71 ⋊ C2×C5 |
| Hall | C5×C7×C71⋊C5 ⋊ C2 |
| Hall | C5×C71⋊C5 ⋊ D7 |
| Hall | C7×C71 ⋊ C5×D5 |
| Sylow | C71 ⋊ C5×D35 |
| Sylow | C7 ⋊ C5⋊(D71⋊C5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C71 | C2×C5 |
| LCS | G ▷ C5×C7×C71 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2485 |
Polycyclic presentation:
2,5^2,7,71|c^a=c^4,d^a=d^6,e^a=e^70,e^b=e^57340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24850, 34);