Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊#64480 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3×C5 |
| unambiguous semidirect product | C3⋊#64480 |
| Fitting, socle | C3×C52 ⋊ Dic3 |
| derived, Hall | C3×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C3×C52⋊C3 | C4 |
| Fitting, socle | C3×C52 | Dic3 |
| prime radical, cosocle | C3×(C5⋊D5)⋊C3 | C2 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 45 |
Polycyclic presentation:
2^2,3^2,5^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^3,e^b=e^4,f^b=f^4,e^c=e^2f^4,f^c=e^2f^218 conjugacy classes — view the full character table.
| maximal subgroup of | #14268376, (#1043⋊C3)⋊D3, D3×#64480, … |
| maximal normal subgroup of | #14268376, (#1043⋊C3)⋊D3, D3×#64480, … |
| maximal quotient of | C3⋊#10597074, C2×C3⋊#64480, C13×C3⋊#64480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 90);