Finite Group DatabasebetaFinite Group Databasebeta| order | 24900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C83⋊#1042) |
| unambiguous semidirect product | C83⋊(C3⋊#1042) |
| Fitting, socle, derived, Hall | C3×C52×C83 ⋊ C4 |
| Hall | C52×C83 ⋊ Dic3 |
| Hall | C3×C83 ⋊ #1042 |
| Sylow | C83 ⋊ C3⋊#1042 |
| Hall | C3×C52 ⋊ Dic83 |
| Sylow | C52 ⋊ Dic249 |
| Sylow | C3 ⋊ C83⋊#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C83 | C4 |
| prime radical, cosocle | C3×C5×D5×C83 | C2 |
| LCS | G ▷ C3×C52×C83 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4980 |
Polycyclic presentation:
2^2,3,5^2,83|a^2=b,c^a=c^2,d^a=d^2,e^a=e^4,f^a=f^82,d^b=d^42493 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24900, 84);