Finite Group DatabasebetaFinite Group Databasebeta| order | 900 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C52×C3⋊Dic3 |
| unambiguous semidirect product | C3⋊(C52×Dic3) |
| derived, Sylow | C32 ⋊ C4×C52 |
| Hall | C32×C52 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | C3⋊D3 |
| commutator, hypocenter | C32 | C4×C52 |
| Frattini | C2 | C52×C3⋊D3 |
| Fitting, socle, prime radical | C2×C32×C52 | C2 |
| cosocle | C2×C32 | C2×C52 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C52 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 900 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×#622, C5×#67126, #14268214, … |
| maximal normal subgroup of | C52×#622, C5×#67126, #14268214, … |
| maximal quotient of | C52×C3⋊(C3⋊C8), C2×C52×C3⋊Dic3, C52×C13×C3⋊Dic3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(900, 84);