Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊#3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊#64470 |
| derived, Hall | C3×C52⋊C3 ⋊ C4 |
| Sylow | C52 ⋊ C3⋊Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊#3874 |
| commutator, hypocenter | C3×C52⋊C3 | C4 |
| Fitting, socle | C2×C3×C52 | D3 |
| prime radical, cosocle | C2×C3×C52⋊C3 | C2 |
| LCS | G ▷ C3×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
Polycyclic presentation:
2^2,3^2,5^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2f,f^a=e^2f^3,e^c=e^2f^4,f^c=e^2f^248 conjugacy classes — view the full character table.
| maximal subgroup of | #14268144, Dic3×#3874, D3×#64470, … |
| maximal normal subgroup of | #14268144, Dic3×#3874, D3×#64470, … |
| maximal quotient of | C3⋊#10597064, C2×C3⋊#64470, C13×C3⋊#64470, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 74);