Finite Group DatabasebetaFinite Group Databasebeta| order | 24900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D75⋊D83 |
| unambiguous semidirect product | D249⋊D25 |
| unambiguous semidirect product | D2075⋊D3 |
| Fitting, derived, Hall | C3×C25×C83 ⋊ C22 |
| Hall | C25×C83 ⋊ C2×D3 |
| Hall | C3×C83 ⋊ C2×D25 |
| Sylow | C83 ⋊ D3×D25 |
| Hall | C3×C25 ⋊ C2×D83 |
| Sylow | C25 ⋊ D3×D83 |
| Sylow | C3 ⋊ D25×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C25×C83 | C22 |
| Frattini | C5 | D15⋊D83 |
| socle | C3×C5×C83 | C2×D5 |
| LCS | G ▷ C3×C25×C83 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6225 |
Polycyclic presentation:
2^2,3,5,83,5|d^5=f^4,d^a=d^4f,e^a=e^82,f^a=f^4,c^b=c^2,d^b=d^4f,f^b=f^41641 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24900, 20);