Finite Group DatabasebetaFinite Group Databasebeta| order | 1476 |
| isoclinism | isoclinic class of C3⋊D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊Dic123 |
| derived, Hall | C32×C41 ⋊ C4 |
| Sylow | C41 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ Dic41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊D123 |
| commutator, hypocenter | C32×C41 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C32×C41 | C2 |
| LCS | G ▷ C32×C41 | |
| UCS | C1 ◁ C2 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1476 |
Polycyclic presentation:
2^2,3^2,41|a^2=b,c^a=c^2,d^a=d^2,e^a=e^40372 conjugacy classes — view the full character table.
| maximal subgroup of | C11×C3⋊Dic123, C3⋊Dic1353, C13×C3⋊Dic123, … |
| maximal normal subgroup of | C11×C3⋊Dic123, C13×C3⋊Dic123, C17×C3⋊Dic123, … |
| maximal quotient of | C11×C3⋊Dic123, C3⋊Dic1353, C13×C3⋊Dic123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1476, 17);