Finite Group DatabasebetaFinite Group Databasebeta| order | 1908 |
| isoclinism | isoclinic class of (C3⋊D3)⋊D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊D53 |
| unambiguous semidirect product | D159⋊D3 |
| Fitting, socle, derived, Hall | C32×C53 ⋊ C22 |
| Sylow | C53 ⋊ D32 |
| Sylow | C32 ⋊ C2×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C53 | C22 |
| LCS | G ▷ C32×C53 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 318 |
Polycyclic presentation:
2^2,3^2,53|c^a=c^2,e^a=e^52,c^b=c^2,d^b=d^2165 conjugacy classes — view the full character table.
| maximal subgroup of | C7×(C3⋊D3)⋊D53, D159⋊D21, (C3⋊D3)⋊D371, … |
| maximal normal subgroup of | C7×(C3⋊D3)⋊D53, C11×(C3⋊D3)⋊D53, (C3⋊D3)⋊(D53⋊C13), … |
| maximal quotient of | C7×(C3⋊D3)⋊D53, D159⋊D21, (C3⋊D3)⋊D371, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1908, 29);