Finite Group DatabasebetaFinite Group Databasebeta| order | 24900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C83⋊#64480 |
| Fitting, socle, Hall | C52×C83 ⋊ Dic3 |
| derived, Hall | C52⋊C3×C83 ⋊ C4 |
| Sylow | C83 ⋊ #64480 |
| Hall | C52⋊C3 ⋊ Dic83 |
| Sylow | C52 ⋊ Dic249 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C52⋊C3×C83 | C4 |
| Fitting, socle | C52×C83 | Dic3 |
| prime radical, cosocle | C83×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C52⋊C3×C83 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1245 |
Polycyclic presentation:
2^2,3,83,5^2|a^2=b,c^a=c^2,d^a=d^82,e^a=e^3,f^a=ef^2,e^b=e^4,f^b=f^4,e^c=ef,f^c=e^2f^3418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24900, 52);