Finite Group DatabasebetaFinite Group Databasebeta| order | 24900 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C83⋊(#1039⋊C3) |
| unambiguous semidirect product | (C83⋊#1039)⋊C3 |
| derived, Hall | C52×C83 ⋊ C3×C4 |
| Hall | C83⋊#1039 ⋊ C3 |
| Hall | C52⋊C3×C83 ⋊ C4 |
| Sylow | C83 ⋊ #1039⋊C3 |
| Hall | C52⋊C3 ⋊ Dic83 |
| Sylow | C52 ⋊ C3×Dic83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C83⋊((C5⋊D5)⋊C3) |
| commutator, hypocenter | C52×C83 | C3×C4 |
| Fitting, socle, cosocle | C2×C52×C83 | C2×C3 |
| prime radical | C2×C52⋊C3×C83 | C2 |
| LCS | G ▷ C52×C83 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4980 |
Polycyclic presentation:
2,3,5^2,83,2|a^2=f,c^a=c^4,d^a=d^4,e^a=e^82,c^b=cd,d^b=c^2d^3922 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24900, 33);