Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊((C5⋊D5)⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊(#1039⋊C3) |
| unambiguous semidirect product | (C3⋊#1039)⋊C3 |
| derived | C3×C52 ⋊ C3×C4 |
| Hall | C3×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊((C5⋊D5)⋊C3) |
| commutator, hypocenter | C3×C52 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C52 | C2×C3 |
| prime radical | C2×C3×C52⋊C3 | C2 |
| LCS | G ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2,3,2,3,5^2|a^2=c,d^a=d^2,e^a=e^4,f^a=f^4,e^b=e^3f^3,f^b=e^4f42 conjugacy classes — view the full character table.
| maximal subgroup of | #14268151, #14268152, #14268153, … |
| maximal normal subgroup of | #14268151, #14268152, #14268153, … |
| maximal quotient of | C3⋊(#6029⋊C3), C2×C3⋊(#1039⋊C3), C13×C3⋊(#1039⋊C3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 77);